Algebra II Chapter 7 Review

Logarithm and Function Basics

1

Find the inverse function of f(x) = x - 3 / 2x + 5.

f^-1(x) = -5x - 3 / 2x -1

2

Find the inverse function of f(x) = 7x³ - 9.

f^-1(x) = ∛x + 9 / 7

3

Determine algebraically if the following equation is a one-to-one function: x - 3 = y³ + 2.

One-to-one function

4

In the logarithmic expression log₅ 125 = 3, which numerical value is the argument?

125

5

A function and its inverse are reflected across this line when graphed together on the Cartesian Plane.

Axis of Symmetry

Exponential and Logarithmic Form

1

Convert the following from exponential form to logarithmic form: 3³ = 27.

log₃ 27 = 3

2

Convert the following from logarithmic form to exponential form: log₂ 64 = 6.

2⁶ = 64

3

Convert the following from exponential form to logarithmic form: 5⁴ = 625.

log₅ 625 = 4

4

Convert the following from logarithmic form to exponential form: log₇ 2,401 = 4.

7⁴ = 2,401

5

Convert the following from exponential form to logarithmic form: 8^x = 4,096.

log₈ 4,096 = x

Expanding and Condensing Logarithms

1

Expand the following logarithmic expression: log (x⁴y⁷z²).

4 log x + 7 log y + 2 log z

2

Condense the following logarithmic expression: 15 log₇ k + 8 log₇ m.

log₇ k¹⁵m⁸

3

Expand the following logarithmic expression: log (x⁴ / yz⁹).

4 log x - log y - 9 log z

4

Condense the following logarithmic expression: 3 log x - 8 log y + 2 log z.

log x³z² / y⁸

5

Condense the following logarithmic expression: 1/2 log x - 12 log y.

log √x / y¹²

Logarithmic and Exponential Equations

1

Solve the following for x: 9^x = 729.

x = 3

2

Solve the following for x: log₂ (x - 7) = log₂ 3

x = 10

3

Solve the following for x: 7^{x + 2} = 16,807

x = 3

4

Solve the following for x: log(2x - 3) = log(x + 2).

x = 5

5

Solve the following for x: 2 log x + log 4 = log 64

x = ± 4

Logarithmic Word Problems

1

What is the sound level of a sound with an intensity of 9.8 x 104 W/m²? Round the answer to the nearest tenth. Use the following formula to answer the question: (10 dB) log I / I₀ where I₀ = 10^-12 W/m².

159.9 dB

3

What is the sound level of a sound with an intensity of 2.4 x 10^-5 W/m²? Round the answer to the nearest tenth. Use the following formula to answer the question: (10 dB) log I / I₀ where I₀ = 10^-12 W/m².

63.8 dB

5

A principal of $1,000 was invested at 5% interest rate for 18 years. Find the final balance for simple interest, compound interest to be compounded yearly, monthly, and daily, and continuously compounding interest. Use the formulas on page 361 of your textbook to solve.

Simple Interest = $1,900

Compounded Yearly = $2,406.62

Compounded Monthly = $2,455.01

Compounded Daily = $2,459.45

Compounded Continuously = $2,459.60