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log_(5)625=

$\log _{5} 625=$

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Convert between exponential and logarithmic form: all bases

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Q.

\log _{5} 625=

Identify base, number, and unknown exponent: Identify the base ( $b$ ), the number ( $x$ ), and the unknown exponent ( $y$ ) in the logarithmic equation $\log_{5}625 = y$ . $\newline$ Here, $b = 5$ and $x = 625$ . We need to find the value of $y$ such that $5^y = 625$ .
Recall logarithm and exponential form: Recall that the logarithm $\log_{b}x = y$ is equivalent to the exponential form $b^{y} = x$ . We need to find the power $y$ to which the base $5$ must be raised to get $625$ .
Determine if $625$ is a power of $5$ : Determine if $625$ is a power of $5$ . We know that $5^2 = 25$ and $5^4 = 625$ . $\newline$ Therefore, $5$ raised to the power of $4$ equals $625$ .
Write exponential equation using base $5$ and exponent $4$ : Write the exponential equation using the base $5$ and the exponent $4$ to equal $625$ . $\newline$ The equation is $5$ ^ $4$ = $625$ .
Value of y in logarithmic equation: Since $5^4 = 625$ , the logarithmic equation $\log_{5}625$ equals $4$ . $\newline$ This means that the value of $y$ in the equation $\log_{5}625 = y$ is $4$ .

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