What is the limit as x approaches 0 of (a^x-1)/x ?

The limit as x approaches 0 of (a^x-1)/x is ln(a)

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limit as x approaches 0 of (a^x-1)/x

x \to 0 lim (\frac{a ^{x} - 1}{x})

ln (a)

Solution steps

x \to 0 lim (\frac{a ^{x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{a ^{x} ln ( a )}{1})

= x \to 0 lim (\frac{a ^{x} ln ( a )}{1})

Plug in the value

x = 0

= \frac{a ^{0} ln ( a )}{1}

Simplify

= ln (a)

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What is the limit as x approaches 0 of (a^x-1)/x ?
The limit as x approaches 0 of (a^x-1)/x is ln(a)