Question

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

\\(\bigcirc\\) \\(\log_{15} 5\\)
\\(\bigcirc\\) \\(\log_{15} 6\\)
\\(\bigcirc\\) \\(2 \log_{15} 3\\)
\\(\bigcirc\\) \\(3 \log_{15} 2\\)

Explanation:

⚡ Using what you learned: properties of logarithms

Step 1: Identify the power property of logarithms

The power property of logarithms states:

$$ \log_{b}(x^{y}) = y \log_{b}(x) $$

Step 2: Apply the property to the given expression

Given expression:

$$ \log_{15}(2^{3}) $$

Identify the components:

• Base \( b = 15 \)
• Argument base \( x = 2 \)
• Exponent \( y = 3 \)

Apply the rule by bringing the exponent to the front:

$$ 3 \log_{15}(2) $$

Answer:

\( 3 \log_{15}(2) \)