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evaluate \\(\\log_{12} y^2\\), given \\(\\log_{12} y = 16\\). \\(\\bigc…

Question

evaluate \\(\log_{12} y^2\\), given \\(\log_{12} y = 16\\).

\\(\bigcirc\\) 4
\\(\bigcirc\\) 32
\\(\bigcirc\\) 256
\\(\bigcirc\\) 65,536

Explanation:

⚡ Using what you learned: properties of logarithms

Step 1: Apply the Power Property of Logarithms

$$ \log_{12} y^2 = 2 \log_{12} y $$

Step 2: Substitute the Given Value

Given that \(\log_{12} y = 16\):

$$ 2 \log_{12} y = 2(16) = 32 $$

Answer:

32