What is the limit as x approaches 0 of (5^x-13^x)/x ?

The limit as x approaches 0 of (5^x-13^x)/x is ln(5)-ln(13)

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limit as x approaches 0 of (5^x-13^x)/x

x \to 0 lim (\frac{5 ^{x} - 1 3 ^{x}}{x})

ln (5) - ln (13)

Decimal

- 0.95551 \dots

Solution steps

x \to 0 lim (\frac{5 ^{x} - 1 3 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{5 ^{x} ln ( 5 ) - 1 3 ^{x} ln ( 13 )}{1})

= x \to 0 lim (\frac{5 ^{x} ln ( 5 ) - 1 3 ^{x} ln ( 13 )}{1})

Plug in the value

x = 0

= \frac{5 ^{0} ln ( 5 ) - 1 3 ^{0} ln ( 13 )}{1}

Simplify

\frac{5 ^{0} ln ( 5 ) - 1 3 ^{0} ln ( 13 )}{1} : ln (5) - ln (13)

= ln (5) - ln (13)

x \to 0 lim (x \cdot sin (\frac{1}{x}))

\frac{\partial}{\partial x} (ln (x) - 4)

\frac{d}{d x} (y^{5} sin (5 x))

\frac{\partial}{\partial x} (4 sin (4 x) e^{3 x})

n = 1 \sum \infty \frac{5}{4 ^{n - 1}}

What is the limit as x approaches 0 of (5^x-13^x)/x ?
The limit as x approaches 0 of (5^x-13^x)/x is ln(5)-ln(13)