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Solve for a positive value of
x.

log_(8)(64)=x
Answer:

Solve for a positive value of $x$ . $\newline$ $\log _{8}(64)=x$ $\newline$ Answer:

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Product property of logarithms

Full solution

Q. Solve for a positive value of

x

.

\newline

\log _{8}(64)=x

\newline

Answer:

Understand the logarithmic equation: Understand the logarithmic equation. $\newline$ The equation $\log_{8}(64) = x$ can be written as $\log_{8}(64) = x$ . This means that $8$ raised to the power of $x$ equals $64$ .
Convert to exponential form: Convert the logarithmic equation to an exponential form. $\newline$ Using the definition of a logarithm, we can rewrite the equation as $8^x = 64$ .
Recognize $64$ as power of $8$ : Recognize that $64$ is a power of $8$ . Since $64$ is $8$ squared ( $8^2$ ), we can write the equation as $8^x = 8^2$ .
Equate the exponents: Equate the exponents. $\newline$ Since the bases are the same $8$ , the exponents must be equal for the equation to hold true. Therefore, $x = 2$ .

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