Multiple Choice
Rewrite the sum as a single logarithm. 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.
A
B
C
D
Verified step by step guidance1
Recall the logarithm property for a quotient: \(\log_{b}\left(\frac{M}{N}\right) = \log_{b}M - \log_{b}N\). This means you can rewrite the log of a fraction as the difference of two logs.
Apply this property to the given expression \(\log_{12}\left(\frac{1}{4}\right)\) by identifying \(M = 1\) and \(N = 4\). So, rewrite it as \(\log_{12}1 - \log_{12}4\).
Evaluate \(\log_{12}1\). Since the logarithm of 1 in any base is always 0 (because \(b^0 = 1\)), this term simplifies to 0.
After simplification, the expression becomes \(0 - \log_{12}4\), which can be written simply as \(-\log_{12}4\).
Thus, the original logarithmic expression is rewritten as a single negative logarithm: \(-\log_{12}4\).
Related Videos
Related Practice