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 sum as a single logarithm. Further simplify if possible.
A
B
C
D
Verified step by step guidance1
Recall the logarithm property that states the sum of logarithms with the same base can be rewritten as the logarithm of the product of their arguments: \(\log_b A + \log_b B = \log_b (A \times B)\).
Identify the base and the arguments in the given expression: the base is 5, the first argument is \(\frac{1}{3}\), and the second argument is \$12y$.
Apply the product rule for logarithms to combine the two logarithms into one: \(\log_5 \frac{1}{3} + \log_5 12y = \log_5 \left( \frac{1}{3} \times 12y \right)\).
Multiply the arguments inside the logarithm: \(\frac{1}{3} \times 12y = 4y\), so the expression becomes \(\log_5 (4y)\).
Check if the argument inside the logarithm can be simplified further; since \$4y$ is already in simplest form, the final expression is \(\log_5 (4y)\).
Related Videos
Related Practice