What is the limit as x approaches 0 of (6^x-5^x)/x ?

The limit as x approaches 0 of (6^x-5^x)/x is ln(6)-ln(5)

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limit as x approaches 0 of (6^x-5^x)/x

x \to 0 lim (\frac{6 ^{x} - 5 ^{x}}{x})

ln (6) - ln (5)

Decimal

0.18232 \dots

Solution steps

x \to 0 lim (\frac{6 ^{x} - 5 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{6 ^{x} ln ( 6 ) - 5 ^{x} ln ( 5 )}{1})

= x \to 0 lim (\frac{6 ^{x} ln ( 6 ) - 5 ^{x} ln ( 5 )}{1})

Plug in the value

x = 0

= \frac{6 ^{0} ln ( 6 ) - 5 ^{0} ln ( 5 )}{1}

Simplify

\frac{6 ^{0} ln ( 6 ) - 5 ^{0} ln ( 5 )}{1} : ln (6) - ln (5)

= ln (6) - ln (5)

f (x) = \frac{x - 3}{x + 3}

\frac{\partial}{\partial y} (\frac{x}{5 + y})

x \to - 1 lim (x - 1)

\frac{d ^{2}}{d t ^{2}} x + 5 \frac{d}{d t} x + 2 x = 0

\frac{\partial}{\partial y} (ln (x^{3} + y^{2}) - ln (x y))

What is the limit as x approaches 0 of (6^x-5^x)/x ?
The limit as x approaches 0 of (6^x-5^x)/x is ln(6)-ln(5)