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 Notation

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)

\frac{d}{d x} (\frac{50 x}{0.01 x ^{2} + 1})

\int (x^{2} + 1)^{- \frac{3}{2}} d x

f (x) = x^{4} - 4 x^{3}

\int x \cdot 1 - x^{4} d x

n = 0 \sum \infty (\frac{1}{2})^{n + 1}

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)