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

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

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

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

- 6

Solution steps

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

Simplify

\frac{1}{x} ln (1 - 6 x) : \frac{ln ( 1 - 6 x )}{x}

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{- \frac{6}{1 - 6 \cdot 0}}{1}

Simplify

\frac{- \frac{6}{1 - 6 \cdot 0}}{1} : - 6

= - 6

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