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

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

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

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

ln (z)

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

= ln (z)

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