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Solve the following logarithm problem for the positive solution for
x.

log_(64)x=-(1)/(3)
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{64} x=-\frac{1}{3}$ $\newline$ Answer:

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Quotient property of logarithms

Full solution

Q. Solve the following logarithm problem for the positive solution for

x

.

\newline

\log _{64} x=-\frac{1}{3}

\newline

Answer:

Understand the logarithmic equation: Understand the logarithmic equation. $\newline$ We have the equation $\log_{64}(x) = -\left(\frac{1}{3}\right)$ . This means we are looking for a number $x$ such that when we raise $64$ to the power of $-\left(\frac{1}{3}\right)$ , we get $x$ .
Convert to exponential form: Convert the logarithmic equation to exponential form. $\newline$ Using the definition of a logarithm, we can rewrite the equation in exponential form: $64^{-(1/3)} = x$ .
Calculate value of $64^{-(1/3)}$ : Calculate the value of $64^{-(1/3)}$ . Since $64$ is $4^3$ , we can rewrite $64^{-(1/3)}$ as $(4^3)^{-(1/3)}$ . By the power of a power rule, this simplifies to $4^{-1}$ , which is equal to $1/4$ .
Conclude the solution: Conclude the solution. $\newline$ Therefore, the positive solution for $x$ is $x = \frac{1}{4}$ .

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