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How do you prove that

\(\large{b^{\log_b a}=a}\)?

An algebraic proof would be good.

Note by Bloons Qoth 3 months ago

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Let \(x=\log_{b} a \)

Then, \[ x=\log_{b} a \implies b^{x} = a \quad (\text{ by definition }) \\\implies b^{\log_{b} a} = a \quad (\text{ substituting } x) \] – Deeparaj Bhat · 3 months ago

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We can prove this algebraically if we want to. But why do that? Isn't this obvious? – Agnishom Chattopadhyay · 3 months ago

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TopNewestLet \(x=\log_{b} a \)

Then, \[ x=\log_{b} a \implies b^{x} = a \quad (\text{ by definition }) \\\implies b^{\log_{b} a} = a \quad (\text{ substituting } x) \] – Deeparaj Bhat · 3 months ago

Log in to reply

We can prove this algebraically if we want to. But why do that? Isn't this obvious? – Agnishom Chattopadhyay · 3 months ago

Log in to reply