Logarithmic to Exponential Conversion Worksheet
Convert logarithmic equations to exponential form and vice versa. Practice with various bases and arguments.
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Logarithmic to Exponential Conversion
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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.
True
False
2. If 3⁻² = 1/9, then log₃(1/9) = 2.
True
False
3. The base of the natural logarithm (ln) is 10.
True
False
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.