What is the value of log_(4)root(5)(4) ? Answer:

Identify Property: Identify the property of logarithms to simplify the expression. The fifth root of 4 can be written as 4^(1/5). We can use the power property of logarithms, which states that log base b of (a^c) is equal to c * log base b of a.Apply Power Property: Apply the power property to the logarithmic expression. log_(4)(4^(1/5)) becomes (1/5) * log_(4)(4).Simplify Logarithm: Simplify the logarithm log_(4)(4). Since the base of the logarithm and the number are the same, log_(4)(4) is equal to 1.Multiply Results: Multiply the result from Step 3 by the fraction from Step 2. (1/5) * 1 = 1/5.Conclude Final Answer: Conclude the final answer. The value of log base 4 of the fifth root of 4 is 1/5.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the value of
log_(4)root(5)(4) ?
Answer:

Evaluate. $\newline$ $\log _{4} \sqrt[5]{4}$ $\newline$ Write your answer in simplest form.

View step-by-step help

Home

Math Problems

Precalculus

Product property of logarithms

Full solution

Q. Evaluate.

\newline

\log _{4} \sqrt[5]{4}

\newline

Write your answer in simplest form.

Identify Property: Identify the property of logarithms to simplify the expression. $\newline$ The fifth root of $4$ can be written as $4^{(1/5)}$ . We can use the power property of logarithms, which states that $\log_b(a^c) = c \cdot \log_b(a)$ .
Apply Power Property: Apply the power property to the logarithmic expression. $\newline$ $\log_{4}(4^{\frac{1}{5}})$ becomes $\frac{1}{5} \times \log_{4}(4)$ .
Simplify Logarithm: Simplify the logarithm $\log_{4}(4)$ . $\newline$ Since the base of the logarithm and the number are the same, $\log_{4}(4)$ is equal to $1$ .
Multiply Results: Multiply the result from Step $3$ by the fraction from Step $2$ . $\newline$ $(\frac{1}{5}) \times 1 = \frac{1}{5}$ .
Conclude Final Answer: Conclude the final answer. $\newline$ The value of $\log_{4} \sqrt[5]{4}$ is $\frac{1}{5}$ .