Mathematics

Problem

b>0

and

b\neq1

, which one of the following must be true whenever

b^{x}=b^{k}

? a)

x=\log_{b} k

x=k

x=k+1

x=\dfrac{k}{\ln b}

Intuitive explanation

The key insight is that exponential functions with a fixed positive base are one-to-one: each output value comes from exactly one input. So if two powers of the same base are equal, their exponents must be identical. This is the fundamental property that lets you "cancel" the base and equate what's in the exponent—no other relationship between $x$ and $k$ is forced by the equation.

Intuitive explanation

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