What is the limit as x approaches 0 of (12^x-5^x)/x ?

The limit as x approaches 0 of (12^x-5^x)/x is ln(12)-ln(5)

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limit as x approaches 0 of (12^x-5^x)/x

x \to 0 lim (\frac{1 2 ^{x} - 5 ^{x}}{x})

ln (12) - ln (5)

Decimal Notation

0.87546 \dots

Solution steps

x \to 0 lim (\frac{1 2 ^{x} - 5 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1 2 ^{x} ln ( 12 ) - 5 ^{x} ln ( 5 )}{1})

= x \to 0 lim (\frac{1 2 ^{x} ln ( 12 ) - 5 ^{x} ln ( 5 )}{1})

Plug in the value

x = 0

= \frac{1 2 ^{0} ln ( 12 ) - 5 ^{0} ln ( 5 )}{1}

Simplify

\frac{1 2 ^{0} ln ( 12 ) - 5 ^{0} ln ( 5 )}{1} : ln (12) - ln (5)

= ln (12) - ln (5)

\frac{d}{d x} (\frac{2 x}{4 x ^{2} + 4})

\int 20 x^{2} + 3 x - 9 d x

\int (6 x^{3} + 3 x^{2}) d x

ln (sec (x))

x \to 0 lim (x^{2} cos (\frac{6}{x}))

What is the limit as x approaches 0 of (12^x-5^x)/x ?
The limit as x approaches 0 of (12^x-5^x)/x is ln(12)-ln(5)