Recognizing Power of 4: We recognize that 16 is a power of 4, specifically 4 squared. Calculation: $ 16 = 4^2 $ Math error check: Using Change of Base Formula: We can use the change of base formula for logarithms, which states that $ \frac{\log(a)}{\log(b)} = \log_b(a) $. Calculation: $ \frac{\log(16)}{\log(4)} = \log_4(16) $ Math error check: Substituting in Logarithm: Now we substitute 16 with $ 4^2 $ in the logarithm. Calculation: $ \log_4(4^2) $ Math error check: Simplifying Expression: Using the property of logarithms that $ \log_b(b^x) = x $, we can simplify the expression. Calculation: $ \log_4(4^2) = 2 $ Math error check:

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$\frac{\log(16)}{\log(4)}$

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Precalculus

Quotient property of logarithms

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\frac{\log(16)}{\log(4)}

Recognizing Power of $4$ : We recognize that $16$ is a power of $4$ , specifically $4$ squared. $\newline$ Calculation: $16 = 4^2$ $\newline$ Math error check:
Using Change of Base Formula: We can use the change of base formula for logarithms, which states that $\frac{\log(a)}{\log(b)} = \log_b(a)$ . $\newline$ Calculation: $\frac{\log(16)}{\log(4)} = \log_4(16)$ $\newline$ Math error check:
Substituting in Logarithm: Now we substitute $16$ with $4^2$ in the logarithm. $\newline$ Calculation: $\log_4(4^2)$ $\newline$ Math error check:
Simplifying Expression: Using the property of logarithms that $\log_b(b^x) = x$ , we can simplify the expression. $\newline$ Calculation: $\log_4(4^2) = 2$ $\newline$ Math error check: