What is the limit as x approaches 0 of (5^x-1)/x ?

The limit as x approaches 0 of (5^x-1)/x is ln(5)

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limit as x approaches 0 of (5^x-1)/x

x \to 0 lim (\frac{5 ^{x} - 1}{x})

ln (5)

Decimal

1.60943 \dots

Solution steps

x \to 0 lim (\frac{5 ^{x} - 1}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{ln ( 5 ) \cdot 5 ^{x}}{1})

Plug in the value

x = 0

= \frac{ln ( 5 ) \cdot 5 ^{0}}{1}

Simplify

= ln (5)

What is the limit as x approaches 0 of (5^x-1)/x ?
The limit as x approaches 0 of (5^x-1)/x is ln(5)