What is the limit as x approaches 0 of (6^x-1)/x ?

The limit as x approaches 0 of (6^x-1)/x is ln(6)

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limit as x approaches 0 of (6^x-1)/x

x \to 0 lim (\frac{6 ^{x} - 1}{x})

ln (6)

Decimal

1.79175 \dots

Solution steps

x \to 0 lim (\frac{6 ^{x} - 1}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{ln ( 6 ) \cdot 6 ^{x}}{1})

Plug in the value

x = 0

= \frac{ln ( 6 ) \cdot 6 ^{0}}{1}

Simplify

= ln (6)

What is the limit as x approaches 0 of (6^x-1)/x ?
The limit as x approaches 0 of (6^x-1)/x is ln(6)