Find logarithm value: We need to find the value of log_(5)25. The logarithm log_(b)a answers the question: ＂To what power must the base b be raised, to produce the number a?＂Rewrite expression using property: Since 25 is a perfect square and can be expressed as 5^2, we can rewrite the expression using the property of logarithms that states log_(b)(b^x) = x.Substitute 25 in expression: Substitute 25 with 5^2 in the logarithmic expression: log_(5)(5^2).Apply logarithm property: Apply the logarithm property to simplify the expression: log_(5)(5^2) = 2.Final logarithm value: We have found the value of the logarithm: log_(5)25 = 2.

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$\log _{5} 25=$

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Grade 8

Relationship between squares and square roots

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\log _{5} 25=

Find logarithm value: We need to find the value of $\log_{5}25$ . The logarithm $\log_{b}a$ answers the question: ＂To what power must the base $b$ be raised, to produce the number $a$ ?＂
Rewrite expression using property: Since $25$ is a perfect square and can be expressed as $5^2$ , we can rewrite the expression using the property of logarithms that states $\log_{b}(b^x) = x$ .
Substitute $25$ in expression: Substitute $25$ with $5$ ^ $2$ in the logarithmic expression: $\log_{$ $5$ }( $5$ ^ $2$ ).
Apply logarithm property: Apply the logarithm property to simplify the expression: $\log_{5}(5^2) = 2$ .
Final logarithm value: We have found the value of the logarithm: $\log_{5}25 = 2$ .