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

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

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

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

- 2

Solution steps

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

Simplify

\frac{1}{x} ln (1 - 2 x) : \frac{ln ( 1 - 2 x )}{x}

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

= \frac{- \frac{2}{1 - 2 \cdot 0}}{1}

Simplify

\frac{- \frac{2}{1 - 2 \cdot 0}}{1} : - 2

= - 2

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