1. Use the properties of logarithms to expand the following. If possible, write your answer without exponents.

Log₉(x⁵/ y³(z-2)⁷)

Log₂(1 / x³y³)

Solve (5 + 2x) + 4 = x+ 5 for x.

Solve the equation for x. Approximate answers to two decimal places.

a) 50 3(0.78)^x-10 = 21

b) 7^x-2=72

c) 64^(x-5)=2^(4-2x)

d) 5(1.3)^x= 2^(4-2x)

Solve the logarithmic equation. Approximate answers to two decimal places

a) 2 log(x+2)= log(x+*)

b) 5 ln(x)=5

c) log₂(2x)-1=5

d) log(x²+3)=log(x²+2x_1)

Combine each expression as the logarithm of a single expression. Simplify when possible

a) log₇5 +log₇k²

b) log₆ 4e³-log₆2e²

Find C and a so that f(x) = Ca^xsatisfies the given conditions

a) f(-1)= 7/3 and f(2)=63

b)f(-1)=1/9 and f(1)=1

If C grams of salt are added to a sample of water, the amount of B of undissolved salt is modeled by B = Ca^x, where x is time. solve the equation for x.

B=Ca^x<-solve the equation f or x

Evaluate the expression by hand and write your answer as a fraction.(Hint:Use properties of rational exponents)

(8 -1/3 + 27^-1/3)²

Use a calculator to approximate the logarithms to the nearest thousandth.

a) 2 log₅ 130 =

b) log₇ 85 + log₅ 17

c) 2log₆ 15 + ³log₃67