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

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

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

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

ln (2) - ln (3)

Decimal Notation

- 0.40546 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= ln (2) - ln (3)

x \to 1 lim ((x - 1) ln (x - 1))

x \to \infty lim (x^{5 x})

x \to 9 lim (x^{2} + 4)

x \to 2 + lim (x + f (x) (x + 2))

x \to \infty lim (\frac{ln ( 2 + e ^{3 x} )}{ln ( 3 + e ^{2 x} )})

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