What is the limit as x approaches 3 of (ln(x)-ln(3))/(x-3) ?

The limit as x approaches 3 of (ln(x)-ln(3))/(x-3) is 1/3

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limit as x approaches 3 of (ln(x)-ln(3))/(x-3)

x \to 3 lim (\frac{ln ( x ) - ln ( 3 )}{x - 3})

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

x \to 3 lim (\frac{ln ( x ) - ln ( 3 )}{x - 3})

Apply L'Hopital's Rule

: x \to 3 lim (\frac{\frac{1}{x}}{1})

= x \to 3 lim (\frac{\frac{1}{x}}{1})

Plug in the value

x = 3

= \frac{\frac{1}{3}}{1}

Simplify

= \frac{1}{3}

n = 0 \sum \infty e^{- n^{2}}

\frac{\partial}{\partial x} (z^{3} x)

\int 5 sec (x + 3) tan (x + 3) d x

x y^{^{'}} + 3 y = 4 x, y (3) = 6

\frac{\partial}{\partial x} (x^{3} - 6 x y + y^{3})

What is the limit as x approaches 3 of (ln(x)-ln(3))/(x-3) ?
The limit as x approaches 3 of (ln(x)-ln(3))/(x-3) is 1/3