What is the limit as x approaches 0 of x/(ln(5x+1)) ?

The limit as x approaches 0 of x/(ln(5x+1)) is 1/5

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limit as x approaches 0 of x/(ln(5x+1))

x \to 0 lim (\frac{x}{ln ( 5 x + 1 )})

\frac{1}{5}

Decimal Notation

0.2

Solution steps

x \to 0 lim (\frac{x}{ln ( 5 x + 1 )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{\frac{5}{5 x + 1}})

= x \to 0 lim (\frac{1}{\frac{5}{5 x + 1}})

Plug in the value

x = 0

= \frac{1}{\frac{5}{5 \cdot 0 + 1}}

Simplify

= \frac{1}{5}

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What is the limit as x approaches 0 of x/(ln(5x+1)) ?
The limit as x approaches 0 of x/(ln(5x+1)) is 1/5