Question

what is \\(\log_{15} 2^3\\) rewritten using the power property?
\\(\circ\\) \\(\log_{15} 5\\)
\\(\circ\\) \\(\log_{15} 6\\)
\\(\circ\\) \\(2\log_{15} 3\\)
\\(\circ\\) \\(3\log_{15} 2\\)

Explanation:

Step1: Recall power property of logs

The power property of logarithms states that $\log_b a^n = n\log_b a$, where $b>0$, $b
eq1$, and $a>0$.

Step2: Apply the property to $\log_{15} 2^3$

Here, $b = 15$, $a = 2$, and $n = 3$. Using the power property, we rewrite $\log_{15} 2^3$ as $3\log_{15} 2$.

Answer:

D. $3\log_{15}2$ (assuming the last option is D, as per the options: the last option is $3\log_{15}2$)