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 for full credit.

Convert each logarithmic equation to its equivalent exponential form.

1. log₅ 25 = 2 =>  

2. log₂ 8 = 3 =>  

3. log₁₀ 1000 = 3 =>  

4. log₃ (1/9) = -2 =>  

5. log₇ 1 = 0 =>  

Convert each exponential equation to its equivalent logarithmic form.

1. 3⁴ = 81 =>  

2. 10² = 100 =>  

3. 5³ = 125 =>  

4. 2⁻³ = 1/8 =>  

5. e⁰ = 1 =>  

Evaluate the following logarithmic expressions by first converting them to exponential form. Show your work.

1. log₄ 64

2. log₆ 36

3. log₉ (1/81)

Choose the correct exponential form for the given logarithmic expression.

1. logₓ y = z

2. Which of the following is the exponential form of log₄ 16 = 2?

Determine if the following statements are true or false.

1. The exponential form of log₈ 64 = 2 is 8² = 64.

2. The logarithmic form of 7³ = 343 is log₃ 343 = 7.