slove problem step by step

2. Simplify each expression completely a. @ b. @ . Type of Problem: o Evaluate exponential and logarithmic expressions (from Section 4.3-4.4) . Practice Problems: o Same directions for the following: o For a: log4 V2 16 log6 (7V6 ) + log6 (7 ) log,( V8 ) o For b: . 10=log10(36) + log10(9) . 49log7(3) +2log-(2) log4 (24) -3log4 (2)3. Solve the logarithmic equation: . Type of Problem; o Solving logarithmic equations (from Section 4.5) . Practice Problems: logo(x ) - logo (1 + x) =3- log2(x + 6) O log10( x - 1) + log10(5) =2- log10(x) logs (x + 2) + logs(3) = logs(9) + logg(2r - 11)4. The population of a certain rare animal species increases exponentially according to the function P(t) = Poet where Po is the initial population, t is time measured in years, and r is a constant. The population increases from @to @ in @years. What is the population after years? Simplify your answer as much as possible . Type of Problem: o Modeling Exponential Functions (from Section 4.6) . Practice Problems o ". The population increases from 30 to 120 in 2 years. What is the population after 3 years?" o "..The population increases from 10 to 90 in 4 years. What is the population after 2 years?" O ".. The population increases from 20 to 80 in 4 years. What is the population after 6 years?"5. Evaluate each of the following: a. 9 b. 9 . Type of Problem: o Evaluate the trigonometric functions (Section 5.2) . Practice Problems sin 171 6 COS -9TT cot 197T 3 CSC tan 237T 6 sec ( 6TT ) O6. Consider the function f (x) = a. State the period and amplitude b. Graph one period of the function labeling the highest and lowest points . Type of Problem: o Graph a sin or cos function (from Section 5.3) . Tip: o Make sure to draw and label the x-axis and y-axis clearly . Practice Problems o f(x) = 5 sin (x) + 2 o f(x) = 2 sin (--nx ) - 1 o f(x) = -3 cos (x)1. Graph f(x) = @ using transformations. Label the asymptote and two points on your final graph. (the coordinate plane will be larger than this) . Type of Problem: o Graph an exponential function using transformations (Section 4.1-4.2) . Tip: o As usual, the two labeled points are from applying the transformations to the points we focus on, on the original . Practice Problems: o f(x) = -3*-3- 1 o f(x) = -2*+3+1 o f(x) = -2*-1 _2