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Solve for a positive value of
x.

log_(8)(512)=x
Answer:

Solve for a positive value of $x$ . $\newline$ $\log _{8}(512)=x$ $\newline$ Answer:

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Product property of logarithms

Full solution

Q. Solve for a positive value of

x

.

\newline

\log _{8}(512)=x

\newline

Answer:

Recognize Equation Form: Recognize the form of the equation. $\newline$ The equation is in the form of a logarithm with base $8$ and the argument is $512$ . We need to find the exponent $x$ such that $8$ raised to the power of $x$ equals $512$ .
Convert to Exponential: Convert the logarithmic equation to an exponential equation. $\newline$ Using the definition of a logarithm, we can rewrite the equation $\log_{8} 512 = x$ as $8^{x} = 512$ .
Find Common Base: Find a common base for $8$ and $512$ . Both $8$ and $512$ are powers of $2$ . $8$ is $2^3$ and $512$ is $2^9$ . So we can rewrite the equation as $(2^3)^x = 2^9$ .
Simplify Left Side: Simplify the left side of the equation using the power of a power property. $\newline$ Using the power of a power property $(a^b)^c = a^{b*c}$ , we get $2^{3x} = 2^9$ .
Set Exponents Equal: Since the bases are equal, the exponents must be equal. We can now set the exponents equal to each other: $3x = 9$ .
Solve for x: Solve for x. $\newline$ Divide both sides of the equation by $3$ to isolate x: $x = \frac{9}{3}$ .
Calculate x Value: Calculate the value of x. $\newline$ $x = \frac{9}{3} = 3$ .

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