Solve for a positive value of x. log_(8)(64)=x Answer:

Understand the logarithmic equation: Understand the logarithmic equation. The equation log base 8 of 64 equals x can be written as log₈(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. 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. 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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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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Precalculus

Product property of logarithms

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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, $x = 2$ .