Question

cphs : advanced algebra: concepts and connections - block (27.0831030)
properties of logarithms
what is \\(\log_{15} 2^3\\) rewritten using the power property?
\\(\log_{15} 6\\)
\\(\log_{15} 5\\)
\\(3\log_{15} 2\\)
\\(2\log_{15} 3\\)

Explanation:

Step1: Recall the power property of logarithms

The power property of logarithms states that for any positive real numbers \(a\) (where \(a
eq1\)), \(x\), and any real number \(n\), \(\log_{a}x^{n}=n\log_{a}x\).

Step2: Apply the power property to \(\log_{15}2^{3}\)

Here, \(a = 15\), \(x = 2\), and \(n = 3\). Using the power property \(\log_{a}x^{n}=n\log_{a}x\), we substitute these values in. So, \(\log_{15}2^{3}=3\log_{15}2\).

Answer:

\(3\log_{15}2\)