Waste less time on Facebook — follow Brilliant.


How do you prove that

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

An algebraic proof would be good.

Note by Bloons Qoth
1 year ago

No vote yet
1 vote


Sort by:

Top Newest

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 · 1 year ago

Log in to reply

We can prove this algebraically if we want to. But why do that? Isn't this obvious? Agnishom Chattopadhyay · 1 year ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...