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

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

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

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

\frac{1}{a}

Solution steps

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

Apply L'Hopital's Rule

: x \to a lim (\frac{\frac{1}{x}}{1})

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

Plug in the value

x = a

= \frac{\frac{1}{a}}{1}

Simplify

= \frac{1}{a}

\int (\frac{sec ( x )}{tan ( x )})^{4} d x

\frac{d y}{d x} = e^{4 x - 3 y}, y (0) = 2

\int \frac{sin ^{5} ( x )}{cos ( x )} d x

y = x

\frac{\partial}{\partial s} (t^{2} - 2 s^{2})

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