Logarithmic to Exponential Conversion
Convert logarithmic expressions to exponential form and vice versa. Practice understanding the relationship between logarithms and exponents.
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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 where applicable.
1. The logarithmic equation log₂ 8 = 3 can be written in exponential form as .
2. The exponential equation 5² = 25 can be written in logarithmic form as .
3. The base of the logarithm in log₋ x = y is .
4. If log₊ b = c, then in exponential form it is .
1. Which of the following is the correct exponential form of log₃ 81 = 4?
4³ = 81
3⁴ = 81
81⁴ = 3
3¹ = 4
2. The logarithmic form of 10³ = 1000 is:
log₃ 1000 = 10
log₁₀ 3 = 1000
log₁₀ 1000 = 3
log₁₀₀₀ 10 = 3
1. Convert log₇ 49 = 2 to exponential form.
2. Convert 6³ = 216 to logarithmic form.
3. Convert log₄ (1/16) = -2 to exponential form.
4. Convert 2⁻⁵ = 1/32 to logarithmic form.
1. The equation 10⁰ = 1 can be written as log₁₀ 1 = 0.
True
False
2. If log x = y, then x = 10ʸ.
True
False
1. If log₋ 64 = 3, what is the value of b? Explain how you found your answer.
2. If 4ʸ = 1/256, write this in logarithmic form and find the value of y.
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