What’s the inverse operation of exponents?

You know, like addition is the inverse operation of subtraction, vice versa, multiplication is the inverse of division, vice versa , square is the inverse of square root, vice versa.

What’s the inverse operation of exponents (exponents: 3^5)

Answer

Addition and multiplication are commutative, so there is just one inverse function.

Exponents are not commutative; 2^8 \not= 8^2. So we need two different inverse functions.

Given b^e = r, we have the “nth root” operation, b = \sqrt[e] r. It turns out that this can actually be written as an exponent itself: \sqrt[e] r = r^{1/e}.

Again, given b^e = r, we have e = \log_b r, the “base-b logarithm of r“.

Attribution
Source : Link , Question Author : warspyking , Answer Author : MathematicalOrchid

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