Evaluate: log_(16)((1)/(64)) Answer:

Identify base and argument: Identify the base and the argument of the logarithm. We are given the logarithm log base 16 of 1/64. We need to evaluate this logarithm.Express argument as power: Express the argument as a power of the base. We know that 64 is 2^6, and 16 is 2^4. Therefore, we can express 1/64 as (2^4)^(-3/2), since (2^4)^(3/2) = 2^6 = 64.Apply change of base formula: Apply the change of base formula. Using the change of base formula, we can write log base 16 of (2^4)^(-3/2) as (log base 16 of 2^4) * (-3/2).Simplify expression: Simplify the expression. Since 16 is 2^4, log base 16 of 2^4 is 1. Therefore, our expression simplifies to 1 * (-3/2), which is -3/2.

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Evaluate: $\newline$ $\log _{16} \frac{1}{64}$ $\newline$ Answer:

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Precalculus

Quotient property of logarithms

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Q. Evaluate:

\newline

\log _{16} \frac{1}{64}

\newline

Answer:

Identify base and argument: Identify the base and the argument of the logarithm. $\newline$ We are given the logarithm $\log_{16} \frac{1}{64}$ . We need to evaluate this logarithm.
Express argument as power: Express the argument as a power of the base. $\newline$ We know that $64$ is $2^6$ , and $16$ is $2^4$ . Therefore, we can express $\frac{1}{64}$ as $(2^4)^{-\frac{3}{2}}$ , since $(2^4)^{\frac{3}{2}} = 2^6 = 64$ .
Apply change of base formula: Apply the change of base formula. $\newline$ Using the change of base formula, we can write $\log_{16} (2^4)^{-\frac{3}{2}}$ as $(\log_{16} 2^4) \cdot (-\frac{3}{2})$ .
Simplify expression: Simplify the expression. $\newline$ Since $16$ is $2^4$ , $\log_{16} 2^4$ is $1$ . Therefore, our expression simplifies to $1 \times (-\frac{3}{2})$ , which is $-\frac{3}{2}$ .