Multiple Choice
Change the following exponential expression to its equivalent logarithmic form.
6. Exponential & Logarithmic Functions
Introduction to Logarithms
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Evaluate the given logarithm.
A
81
B
2
C
– 2
D
9
Verified step by step guidance1
Recognize that the problem involves evaluating the logarithm \( \log_9 \frac{1}{81} \). This means we need to find the exponent to which 9 must be raised to yield \( \frac{1}{81} \).
Recall the property of logarithms: \( \log_b a = x \) implies \( b^x = a \). Here, \( b = 9 \) and \( a = \frac{1}{81} \).
Express \( \frac{1}{81} \) as a power of 9. Notice that \( 81 = 9^2 \), so \( \frac{1}{81} = 9^{-2} \).
Set up the equation based on the logarithmic identity: \( 9^x = 9^{-2} \).
Since the bases are the same, equate the exponents: \( x = -2 \). This is the value of the logarithm \( \log_9 \frac{1}{81} \).
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