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nature of mathematics

Questions and Answers of Nature Of Mathematics

Write each expression in Problems 29–32 in terms of common logarithms, and then give a calculator approximation (correct to four decimal places). a. log, 13 b. log556
Write each expression in Problems 29–32 in terms of common logarithms, and then give a calculator approximation (correct to four decimal places). a. log43.05 b. log 1,513
Write each expression in Problems 33–36 in terms of natural logarithms, and then give a calculator approximation (correct to four decimal places). a. log0.0056 b. logg3 105 88.3
Write each expression in Problems 33–36 in terms of natural logarithms, and then give a calculator approximation (correct to four decimal places). a. log, 10 b. log e
Write each expression in Problems 33–36 in terms of natural logarithms, and then give a calculator approximation (correct to four decimal places). a. log,56 b. log10.85
Write each expression in Problems 33–36 in terms of natural logarithms, and then give a calculator approximation (correct to four decimal places). a. logge b. log1.085,450
Solve the exponential equations in Problems 37–44. Show the approximation you obtain with your calculator without rounding. a. 8 = 3 b. 64* = 5
Solve the exponential equations in Problems 37–44. Show the approximation you obtain with your calculator without rounding. a. et = 4 b. e* = 25
Solve the exponential equations in Problems 37–44. Show the approximation you obtain with your calculator without rounding. a. 10 = 42 b. 100.0234
Solve the exponential equations in Problems 37–44. Show the approximation you obtain with your calculator without rounding. 105x = 5 b. 103 = 0.45
Solve the exponential equations in Problems 37–44. Show the approximation you obtain with your calculator without rounding. a. ex = 8 b. 10 125 =
Solve the exponential equations in Problems 37–44. Show the approximation you obtain with your calculator without rounding. a. 10-2x = 50 b. e-2x = 450
Solve the exponential equations in Problems 37–44. Show the approximation you obtain with your calculator without rounding. a. 105-3x = 0.041 b. 102x-1515 =
Solve the exponential equations in Problems 37–44. Show the approximation you obtain with your calculator without rounding. a. el-2x = 3 b. el-5x = 25
Scientific research has shown that the risk of having an automobile accident increases exponentially as the concentration of alcohol in the blood increases.The blood alcohol concentration is modeled
Scientific research has shown that the risk of having an automobile accident increases exponentially as the concentration of alcohol in the blood increases.The blood alcohol concentration is modeled
Scientific research has shown that the risk of having an automobile accident increases exponentially as the concentration of alcohol in the blood increases.The blood alcohol concentration is modeled
Scientific research has shown that the risk of having an automobile accident increases exponentially as the concentration of alcohol in the blood increases.The blood alcohol concentration is modeled
In 2012 the minimum wage in Arizona was $7.65. If we assume the growth of this minimum wage is exponential and is growing at the rate of 2%, then the length of time until the minimum wage reaches d
In 2012 the minimum wage in California was $8.00. If we assume the growth of this minimum wage is exponential and is growing at the rate of 2%, then the length of time until the minimum wage reaches
In 2012 the minimum wage in Washington state was $9.04. If we assume the growth of this minimum wage is exponential and is growing at the rate of 2%, then the length of time until the minimum wage
In 2012 the minimum wage in Florida was $7.67. If we assume the growth of this minimum wage is exponential and is growing at the rate of 2%, then the length of time until the minimum wage reaches d
Solve the exponential equations in Problems 53–58. Show the approximation you obtain with your calculator without rounding. 2-3 +7 61
Solve the exponential equations in Problems 53–58. Show the approximation you obtain with your calculator without rounding. 3-5 + 30 105
Solve the exponential equations in Problems 53–58. Show the approximation you obtain with your calculator without rounding. 1 + 0.08\360x 360 2
Solve the exponential equations in Problems 53–58. Show the approximation you obtain with your calculator without rounding. (1 + 0.055) 12x = = 2 12
Solve the exponential equations in Problems 53–58. Show the approximation you obtain with your calculator without rounding. Solve P= Poet for t
Solve the exponential equations in Problems 53–58. Show the approximation you obtain with your calculator without rounding. -rt Solve I = Ioe for r
If the earth’s radius is approximately 3,963 mi, and if a hypothetical perpetual water-making machine pours out 1 gallon in the first minute and then doubles its output each minute, in which minute
If the weight of the earth is 5.9 × 1021 metric tons, and if its weight were cut in half each minute, how long would it take for the earth to weigh less than one g?
Evaluate the given expressions. a. log 10 b. In e c. 10log 8.3 d. eln 4.5 e. logg 84.2
Solve the following logarithmic equations: a. Type I: log V3 = x b. Type II: log,6 = 2 c. Type III: In x = 5 d. Type IV: log5x = log, 72
Write each statement as a single logarithm. a. log x + 5 log y - log z b. log 3x - 2 logx + log (x + 3)
The largest number that you can write with three digits is 999. Write this number as a power of 10.
What is a logarithmic equation?
What are the four types of logarithmic equations?
What is the change of base theorem, and why is it important?
Outline a procedure for solving logarithmic equations.
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.A common logarithm is a logarithm in which the base is 2 .
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.A natural logarithm is a logarithm in which the base is 10 .
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.If \(2 \log _{3} 81=8\), then \(\log _{3} 6,561=8\).
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.If \(2 \log _{3} 81=8\), then \(\log _{3} 81=4\).
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.If \(\log _{1.5} 8=x\), then \(x^{1.5}=8\).
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.\(\ln \frac{x}{2}=\frac{\ln x}{2}\)
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.\(\log _{b}(A+B)=\log _{b} A+\log _{b} B\)
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.\(\log _{b} A B=\left(\log _{b} Aight)\left(\log _{b} Bight)\)
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.\(\frac{\log _{b} A}{\log _{b} B}=\log _{b} \frac{A}{B}\)
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.\(\frac{\log A}{\log B}=\frac{\ln A}{\ln B}\)
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.\(\frac{\log _{b} A}{\log _{b} B}=\log _{b}(A-B)\)
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.\(\frac{\log _{b} A}{\log _{b} B}=\log _{b} A-\log _{b} B\)
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.\(\log _{b} N\) is negative when \(N\) is negative.
Classify each of the statements in Problems 5-18 as true or false. If a statement is false, explain why you think it is false.\(\log N\) is negative when \(N>1\).
Find a simplified value for \(x\) in Problems 19-24 by inspection. Do not use a calculator.a. \(e^{\ln 23}\)b. \(10^{\log 3.4}\)c. \(4^{\log _{4} x}\)d. \(\log _{b} b^{x}\)
Find a simplified value for \(x\) in Problems 19-24 by inspection. Do not use a calculator.a. \(\log 10^{4.2}\)b. \(\ln e^{3}\)c. \(\log _{6} 6^{x}\)d. \(b^{\log _{b} x}\)
Find a simplified value for \(x\) in Problems 19-24 by inspection. Do not use a calculator.a. \(\log _{5} 25=x\)b. \(\log _{2} 128=x\)c. \(\log _{3} 81=x\)d. \(\log _{4} 64=x\)
Find a simplified value for \(x\) in Problems 19-24 by inspection. Do not use a calculator.a. \(\log \frac{1}{10}=x\)b. \(\log 10,000=x\)c. \(\log 1,000=x\)d. \(\log \frac{1}{1,000}=x\)
Find a simplified value for \(x\) in Problems 19-24 by inspection. Do not use a calculator.a. \(\log x=5\)b. \(\log _{x} e=1\)c. \(\ln x=2\)d. \(\ln x=3\)
Find a simplified value for \(x\) in Problems 19-24 by inspection. Do not use a calculator.a. \(\ln x=4\)b. \(\ln x=\ln 14\)c. \(\ln 9.3=\ln x\)d. \(\ln 109=\ln x\)
Contract the expressions given in Problems 25-28. That is, use the properties of logarithms to write each expression as a single logarithm with a coefficient of 1.a. \(\log 2+\log 3+\log 4\)b. \(\log
Contract the expressions given in Problems 25-28. That is, use the properties of logarithms to write each expression as a single logarithm with a coefficient of 1.a. \(3 \ln 4-5 \ln 2+\ln 3\)b. \(3
Contract the expressions given in Problems 25-28. That is, use the properties of logarithms to write each expression as a single logarithm with a coefficient of 1.a. \(\ln 3-2 \ln 4+\ln 8\)b. \(\ln
Contract the expressions given in Problems 25-28. That is, use the properties of logarithms to write each expression as a single logarithm with a coefficient of 1.a. \(\log \left(x^{2}-9ight)-\log
The \(\mathrm{pH}\) of a substance measures its acidity or alkalinity. It is found by the formula \[p H=-\log \left[H^{+}ight]\] where \(\left[\mathrm{H}^{+}ight]\)is the concentration of hydrogen
The \(\mathrm{pH}\) of a substance measures its acidity or alkalinity. It is found by the formula \[p H=-\log \left[H^{+}ight]\] where \(\left[\mathrm{H}^{+}ight]\)is the concentration of hydrogen
The \(\mathrm{pH}\) of a substance measures its acidity or alkalinity. It is found by the formula \[p H=-\log \left[H^{+}ight]\] where \(\left[\mathrm{H}^{+}ight]\)is the concentration of hydrogen
The \(\mathrm{pH}\) of a substance measures its acidity or alkalinity. It is found by the formula \[p H=-\log \left[H^{+}ight]\] where \(\left[\mathrm{H}^{+}ight]\)is the concentration of hydrogen
An advertising agency conducted a survey and found that the number of units sold, \(N\), is related to the amount \(a\) spent on advertising (in dollars) by the following formula:\[N=1,500+300 \ln
An advertising agency conducted a survey and found that the number of units sold, \(N\), is related to the amount \(a\) spent on advertising (in dollars) by the following formula:\[N=1,500+300 \ln
Solve the equations in Problems 35-54 by finding the exact solution.a. \(\frac{1}{2} x-2=2\)b. \(\frac{1}{2} \log x-\log 100=2\)
Solve the equations in Problems 35-54 by finding the exact solution.a. \(3+2 x=11\)b. \(\ln e^{3}+2 \log x=11\)
Solve the equations in Problems 35-54 by finding the exact solution.a. \(\frac{1}{2} x=3-x\)b. \(\frac{1}{2} \log _{b} x=3 \log _{b} 5-\log _{b} x\)
Solve the equations in Problems 35-54 by finding the exact solution.a. \(x-2=2\)b. \(\log 10^{x}-2=\log 100\)
Solve the equations in Problems 35-54 by finding the exact solution.a. \(1=x-1\)b. \(\ln e=\ln \frac{\sqrt{2}}{x}-\ln e \)
Solve the equations in Problems 35-54 by finding the exact solution.a. \(1=\frac{3}{2}-x\)b. \(\log 10=\log \sqrt{1,000}-\log x\)
Solve the equations in Problems 35-54 by finding the exact solution.a. \(3-x=1\)b. \(\ln e^{3}-\ln x=1\)
Solve the equations in Problems 35-54 by finding the exact solution.a. \(0+x=2\)b. \(\ln 1+\ln e^{x}=2\)
Solve the equations in Problems 35-54 by finding the exact solution.\(\log (\log x)=1\)
Solve the equations in Problems 35-54 by finding the exact solution.\(\ln [\log (\ln x)]=0\)
Solve the equations in Problems 35-54 by finding the exact solution.\(x^{2} 5^{x}=5^{x}\)
Solve the equations in Problems 35-54 by finding the exact solution.\(x^{2} 3^{x}=9\left(3^{x}ight)\)
Solve the equations in Problems 35-54 by finding the exact solution.\(\log x=1.8+\log 4.8\)
Solve the equations in Problems 35-54 by finding the exact solution.\(\ln x=1.8-\ln 4.8 \quad e^{1.8} / 4.8\)
Solve the equations in Problems 35-54 by finding the exact solution.\(\ln x-\ln 8=12\)
Solve the equations in Problems 35-54 by finding the exact solution.\(\log x+\log 8=12\)
Solve the equations in Problems 35-54 by finding the exact solution.\(\log 2=\frac{1}{4} \log 16-x\)
Solve the equations in Problems 35-54 by finding the exact solution.\(\log _{8} 5+\frac{1}{2} \log _{8} 9=\log _{8} x \quad 15\)
Solve the equations in Problems 35-54 by finding the exact solution.\(\log _{5} 4+\frac{1}{2} \log _{5} 9=\log _{5} x \quad 12\)
Solve the equations in Problems 35-54 by finding the exact solution.\(\log x+\log (x-3)=2 \quad \frac{3+\sqrt{409}}{2}\)
An advertising agency conducted a survey and found that the number of units sold, \(N\), is related to the amount \(a\) spent on advertising (in dollars) by the following formula:\[N=1,500+300 \ln
If we assume the growth of minimum wage is exponential and is growing at the rate of \(2 \%\), then the time \(t\) it takes for a minimum wage of \(w\) dollars to reach \(d\) dollars is given by the
The "forgetting curve" for memorizing nonsense syllables is given by\[R=80-27 \ln t(t \geq 1)\]where \(R\) is the percentage who remember the syllables after \(t\) seconds.a. In how many seconds
The "learning curve" describes the rate at which a person learns certain tasks. If a person sets a goal of typing \(N\) words per minute (wpm), the length of time \(t\) (in days) to achieve this goal
In 1935 Charles Richter and Beno Gütenberg of \(\mathrm{Cal}\) Tech used a new scale for measuring earthquakes in California. This scale is now universally used to measure the strength of
Prove the multiplication law of logarithms using the multiplication law of exponents. That is, prove\[\log _{b} A^{p}=p \log _{b} A \quad \text {} \mathbb{}\]
What do we mean by topology?
Describe topologically equivalent figures.
What is the four-color problem?
What is a tessellation?
In Problems 5–14, there are three figures. In each problem, select two that are topologically equivalent. If none of them are equivalent, then so state. O circle square triangle
In Problems 5–14, there are three figures. In each problem, select two that are topologically equivalent. If none of them are equivalent, then so state. OOO stop sign circle new moon

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