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 Notation

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})

= 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)

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

x \to 0 lim (cos^{\frac{3}{x}} (2 x))

x \to - 3 - lim (\frac{3 x}{9 - x ^{2}})

x \to 0 + lim ((x^{2} + 1) ln (x))

x \to 6 lim (3 x - 4)

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)