What is the limit as x approaches 0 of (2^x-1)/x ?

The limit as x approaches 0 of (2^x-1)/x is ln(2)

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limit as x approaches 0 of (2^x-1)/x

x \to 0 lim (\frac{2 ^{x} - 1}{x})

ln (2)

Decimal

0.69314 \dots

Solution steps

x \to 0 lim (\frac{2 ^{x} - 1}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{ln ( 2 ) \cdot 2 ^{x}}{1})

Plug in the value

x = 0

= \frac{ln ( 2 ) \cdot 2 ^{0}}{1}

Simplify

= ln (2)

What is the limit as x approaches 0 of (2^x-1)/x ?
The limit as x approaches 0 of (2^x-1)/x is ln(2)