Identify base, argument, and unknown exponent: Identify the base (b), the argument (x), and the unknown exponent (y) in the logarithmic equation log_(8)512 = y. In this case, b = 8 and x = 512. We need to find the value of y such that 8^y = 512.Recall logarithms and exponents relationship: Recall the relationship between logarithms and exponents: log_(b)x = y is equivalent to b^y = x. We need to find the value of y that makes the equation 8^y = 512 true.Determine the value of y: Determine the value of y by finding a power of 8 that equals 512. We know that 8^1 = 8, 8^2 = 64, and 8^3 = 512. Therefore, y = 3 because 8^3 = 512.Write the equation in exponential form: Write the original logarithmic equation in exponential form using the value of y found in the previous step. The exponential form of log_(8)512 is 8^3.

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$\log _{8} 512=$

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Algebra 2

Convert between exponential and logarithmic form: all bases

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\log _{8} 512=

Identify base, argument, and unknown exponent: Identify the base (), the argument (), and the unknown exponent () in the logarithmic equation _{( $8$ )} $512$ = . In this case, = $8$ and = $512$ . We need to find the value of such that $8$ ^ = $512$ .
Recall logarithms and exponents relationship: Recall the relationship between logarithms and exponents: $\log_{b}x = y$ is equivalent to $b^{y} = x$ . $\newline$ We need to find the value of $y$ that makes the equation $8^{y} = 512$ true.
Determine the value of $y$ : Determine the value of $y$ by finding a power of $8$ that equals $512$ . $\newline$ We know that $8$ ^ $1$ = $8$ , $8$ ^ $2$ = $64$ , and $8$ ^ $3$ = $512$ . $\newline$ Therefore, $y =$ $3$ because $8$ ^ $3$ = $512$ .
Write the equation in exponential form: Write the original logarithmic equation in exponential form using the value of $y$ found in the previous step. $\newline$ The exponential form of $\log_{8}512$ is $8^3$ .