Multiple Choice
Rewrite the log expression as a sum of multiple logs. Further simplify if possible.
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13. 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 logarithm property for division inside a log: \(\log_b\left(\frac{M}{N}\right) = \log_b M - \log_b N\). This means the log of a quotient can be rewritten as the difference of two logs.
Apply this property to the given expression \(\log_2\left(\frac{x}{6}\right)\) by identifying \(M = x\) and \(N = 6\).
Rewrite the expression as \(\log_2 x - \log_2 6\) using the property from step 1.
Check if further simplification is possible. Since \(x\) and \(6\) are different terms and cannot be simplified further inside the logs, the expression \(\log_2 x - \log_2 6\) is the simplified form.
Thus, the original logarithmic expression is rewritten as a difference of two logarithms with the same base.
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