What is the limit as x approaches 4 of ((ln(x)-ln(4)))/(x-4) ?

The limit as x approaches 4 of ((ln(x)-ln(4)))/(x-4) is 1/4

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limit as x approaches 4 of ((ln(x)-ln(4)))/(x-4)

x \to 4 lim (\frac{( ln ( x ) - ln ( 4 ) )}{x - 4})

\frac{1}{4}

Decimal

0.25

Solution steps

x \to 4 lim (\frac{ln ( x ) - ln ( 4 )}{x - 4})

Apply L'Hopital's Rule

= x \to 4 lim (\frac{\frac{1}{x}}{1})

Plug in the value

x = 4

= \frac{\frac{1}{4}}{1}

Simplify

= \frac{1}{4}

What is the limit as x approaches 4 of ((ln(x)-ln(4)))/(x-4) ?
The limit as x approaches 4 of ((ln(x)-ln(4)))/(x-4) is 1/4