What is the limit as x approaches 0 of (3^x-2^x)/x ?

The limit as x approaches 0 of (3^x-2^x)/x is ln(3)-ln(2)

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limit as x approaches 0 of (3^x-2^x)/x

x \to 0 lim (\frac{3 ^{x} - 2 ^{x}}{x})

ln (3) - ln (2)

Decimal Notation

0.40546 \dots

Solution steps

x \to 0 lim (\frac{3 ^{x} - 2 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 ^{x} ln ( 3 ) - 2 ^{x} ln ( 2 )}{1})

= x \to 0 lim (\frac{3 ^{x} ln ( 3 ) - 2 ^{x} ln ( 2 )}{1})

Plug in the value

x = 0

= \frac{3 ^{0} ln ( 3 ) - 2 ^{0} ln ( 2 )}{1}

Simplify

\frac{3 ^{0} ln ( 3 ) - 2 ^{0} ln ( 2 )}{1} : ln (3) - ln (2)

= ln (3) - ln (2)

\frac{\partial}{\partial x} (\frac{x}{x + 3})

f (x) = \frac{x}{x ^{2} - 1}

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 8 y = 0

\int \frac{9}{x - 4} d x

\frac{d}{d x} (tan (4 x^{5}))

What is the limit as x approaches 0 of (3^x-2^x)/x ?
The limit as x approaches 0 of (3^x-2^x)/x is ln(3)-ln(2)