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

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

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

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

- 2

Solution steps

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