Prove that:b^ _b a =a - Vidyadip

Question

Prove that:$b^{\log _b a}=a$

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Answer

We have to prove that $b^{\log _b a}=a$
i.e., to prove that $\left(\log _b a\right)\left(\log _b b\right)=\log _b a$
(Taking log on both sides with base b)
$ \text { L.H.S. }=\left(\log _b a\right)\left(\log _b b\right)$
$=\log _b a \ldots . .\left[\because \log _b b=1\right]$
$=\text { R.H.S. } $

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