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log_(5)25=

log⁡525= \log _{5} 25=

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Relationship between squares and square rootsright chevron icon

Full solution

Q. log⁡525= \log _{5} 25=
  1. Find logarithm value: We need to find the value of log⁡525\log_{5}25. The logarithm log⁡ba\log_{b}a answers the question: ＂To what power must the base bb be raised, to produce the number aa?＂
  2. Rewrite expression using property: Since 2525 is a perfect square and can be expressed as 525^2, we can rewrite the expression using the property of logarithms that states log⁡b(bx)=x\log_{b}(b^x) = x.
  3. Substitute 2525 in expression: Substitute 2525 with 55^22 in the logarithmic expression: \log_{55}(55^22).
  4. Apply logarithm property: Apply the logarithm property to simplify the expression: log⁡5(52)=2\log_{5}(5^2) = 2.
  5. Final logarithm value: We have found the value of the logarithm: log⁡525=2\log_{5}25 = 2.

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