Logarithmic to Exponential Conversion Worksheet

Logarithmic to Exponential Conversion

Read each question carefully and follow the instructions to convert between logarithmic and exponential forms. Show all your work.

Convert each logarithmic equation to its equivalent exponential form.

1. log₅(25) = 2

2. log₃(81) = 4

3. log₁₀(0.001) = -3

4. ln(e⁷) = 7

5. log₂(1/16) = -4

Convert each exponential equation to its equivalent logarithmic form.

1. 4³ = 64

2. 10⁵ = 100,000

3. 7⁰ = 1

4. e² = x

5. (1/2)⁻³ = 8

Complete the following conversions by filling in the blanks.

1. If log₆(36) = 2, then 6² =  .

2. If 5³ = 125, then log₅(125) =  .

3. logₐ(b) = c is equivalent to  .

4. xʸ = z is equivalent to  .

5. The natural logarithm ln(x) is equivalent to logₑ(x), so ln(10) = y means eʸ =  .

Determine if the following statements are true or false.

1. The equation log₂(8) = 3 is equivalent to 2³ = 8.

2. If 3⁻² = 1/9, then log₃(1/9) = 2.

3. The base of the natural logarithm (ln) is 10.

Answer the following challenge questions.

1. If logₓ(64) = 3, what is the value of x?

2. If 9ʸ = 27, express y in terms of logarithms and then convert to exponential form.