What is the value of log_(4)root(4)(4) ? Answer:

Understand the expression: Understand the expression. We need to find the value of log_(4)root(4)(4), which means we are looking for the exponent that 4 must be raised to in order to get the fourth root of 4.Express as power of 4: Express the fourth root of 4 as a power of 4. The fourth root of 4 can be written as 4^(1/4).Substitute into logarithm: Substitute the expression into the logarithm. Now we have log_(4)(4^(1/4)).Apply power rule: Apply the logarithm power rule. The power rule of logarithms states that log_(b)(a^c) = c * log_(b)(a). In this case, we have log_(4)(4^(1/4)) = (1/4) * log_(4)(4).Evaluate log(4)(4): Evaluate log_(4)(4). Since the base of the logarithm and the number are the same, log_(4)(4) = 1.Multiply by exponent: Multiply the result by the exponent. Now we multiply the result from Step 5 by the exponent from Step 4: (1/4) * 1 = 1/4.Conclude solution: Conclude the solution. The value of log_(4)root(4)(4) is 1/4.

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What is the value of
log_(4)root(4)(4) ?
Answer:

Evaluate. $\newline$ $\log _{4} \sqrt[4]{4}$ $\newline$ Write your answer in simplest form.

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Algebra 1

Multiplication with rational exponents

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Q. Evaluate.

\newline

\log _{4} \sqrt[4]{4}

\newline

Write your answer in simplest form.

Understand the expression: Understand the expression. $\newline$ We need to find the value of $\log_{4}\sqrt[4]{4}$ , which means we are looking for the exponent that $4$ must be raised to in order to get the fourth root of $4$ .
Express as power of $4$ : Express the fourth root of $4$ as a power of $4$ . $\newline$ The fourth root of $4$ can be written as $4^{1/4}$ .
Substitute into logarithm: Substitute the expression into the logarithm. $\newline$ Now we have $\log_{4}(4^{\frac{1}{4}})$ .
Apply power rule: Apply the logarithm power rule. $\newline$ The power rule of logarithms states that $\log_{b}(a^c) = c \cdot \log_{b}(a)$ . In this case, we have $\log_{4}(4^{\frac{1}{4}}) = \frac{1}{4} \cdot \log_{4}(4)$ .
Evaluate $\log_{4}(4)$ : Evaluate $\log_{4}(4)$ . $\newline$ Since the base of the logarithm and the number are the same, $\log_{4}(4) = 1$ .
Multiply by exponent: Multiply the result by the exponent. $\newline$ Now we multiply the result from Step $5$ by the exponent from Step $4$ : $(\frac{1}{4}) \times 1 = \frac{1}{4}$ .
Conclude solution: Conclude the solution. $\newline$ The value of $\log_{4}\sqrt[4]{4}$ is $\frac{1}{4}$ .