Evaluate: log_(4)((1)/(8)) Answer:

Question Prompt: Question prompt: What is the value of the logarithm base 4 of 1/8?Recognize Relationship: Recognize the relationship between the base of the logarithm and the argument. The logarithm log base 4 of 1/8 can be evaluated by expressing 1/8 as a power of 4.Express as Power of 4: Express 1/8 as a power of 4. Since 8 is 2^3, we can write 1/8 as 2^(-3). Now we need to express 2^(-3) as a power of 4. Since 4 is 2^2, we can rewrite 2^(-3) as (2^2)^(-3/2) which is 4^(-3/2).Apply Logarithm: Apply the logarithm. Now that we have expressed 1/8 as 4^(-3/2), we can write the logarithm as log base 4 of 4^(-3/2).Simplify Logarithm: Simplify the logarithm using the property log base b of b^x = x. Using this property, log base 4 of 4^(-3/2) simplifies to -3/2.

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Evaluate: $\newline$ $\log _{4} \frac{1}{8}$ $\newline$ Answer:

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Precalculus

Quotient property of logarithms

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Q. Evaluate:

\newline

\log _{4} \frac{1}{8}

\newline

Answer:

Question Prompt: Question prompt: What is the value of the logarithm base $4$ of $1/8$ ?
Recognize Relationship: Recognize the relationship between the base of the logarithm and the argument. $\newline$ The logarithm $\log_{4} \frac{1}{8}$ can be evaluated by expressing $\frac{1}{8}$ as a power of $4$ .
Express as Power of $4$ : Express $1/8$ as a power of $4$ . Since $8$ is $2^3$ , we can write $1/8$ as $2^{-3}$ . Now we need to express $2^{-3}$ as a power of $4$ . Since $4$ is $2^2$ , we can rewrite $2^{-3}$ as $4$ $1$ which is $4$ $2$ .
Apply Logarithm: Apply the logarithm. $\newline$ Now that we have expressed $\frac{1}{8}$ as $4^{-\frac{3}{2}}$ , we can write the logarithm as $\log_{4} 4^{-\frac{3}{2}}$ .
Simplify Logarithm: Simplify the logarithm using the property $\log_{b} b^{x} = x$ . Using this property, $\log_{4} 4^{(-\frac{3}{2})}$ simplifies to $-\frac{3}{2}$ .