What is the limit as x approaches 0 of (5^x-3^x)/x ?

The limit as x approaches 0 of (5^x-3^x)/x is ln(5)-ln(3)

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limit as x approaches 0 of (5^x-3^x)/x

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

ln (5) - ln (3)

Decimal

0.51082 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= ln (5) - ln (3)

\int (- x^{5} + 6 e^{- 2 x}) d x

(x + y) y^{^{'}} = x - y

\int \frac{1}{x} + 1 d x

\int 3 r^{2} d r

f (x) = x^{2} + 5, at x = 2

What is the limit as x approaches 0 of (5^x-3^x)/x ?
The limit as x approaches 0 of (5^x-3^x)/x is ln(5)-ln(3)