Multiple Choice
Rewrite the log expression as a sum of multiple logs. Further simplify if possible.
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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