Multiple Choice
Rewrite the log expression as a sum of multiple logs. Further simplify if possible.
11. Inverse, Exponential, & Logarithmic Functions
Properties of Logarithms
Multiple Choice
Rewrite the log expression as a difference of multiple logs. Further simplify if possible.
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Verified step by step guidance1
Recall the logarithmic property that states: the logarithm of a quotient can be rewritten as the difference of logarithms. Specifically, for any positive numbers a, b and base c (where c ≠ 1), we have: \(\log_c\left(\frac{a}{b}\right) = \log_c a - \log_c b\).
Identify the components in the given expression \(\log_2\left(\frac{x}{6}\right)\) where \(a = x\) and \(b = 6\), and the base is 2.
Apply the quotient rule for logarithms to rewrite the expression as the difference of two logarithms with the same base: \(\log_2 x - \log_2 6\).
Check if either \(\log_2 x\) or \(\log_2 6\) can be simplified further. Since \(x\) is a variable and 6 is a constant, and 6 is not a power of 2, no further simplification is possible.
Write the final simplified expression as \(\log_2 x - \log_2 6\), which is the difference of two logarithms.
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