What is the limit as x approaches 0 of (8^x-14^x)/x ?

The limit as x approaches 0 of (8^x-14^x)/x is 3ln(2)-ln(14)

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limit as x approaches 0 of (8^x-14^x)/x

x \to 0 lim (\frac{8 ^{x} - 1 4 ^{x}}{x})

3 ln (2) - ln (14)

Decimal Notation

- 0.55961 \dots

Solution steps

x \to 0 lim (\frac{8 ^{x} - 1 4 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 ln ( 2 ) \cdot 8 ^{x} - 1 4 ^{x} ln ( 14 )}{1})

= x \to 0 lim (\frac{3 ln ( 2 ) \cdot 8 ^{x} - 1 4 ^{x} ln ( 14 )}{1})

Plug in the value

x = 0

= \frac{3 ln ( 2 ) \cdot 8 ^{0} - 1 4 ^{0} ln ( 14 )}{1}

Simplify

\frac{3 ln ( 2 ) \cdot 8 ^{0} - 1 4 ^{0} ln ( 14 )}{1} : 3 ln (2) - ln (14)

= 3 ln (2) - ln (14)

\frac{d}{d x} (\frac{1}{5} sin (5 x))

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

\int \frac{4 x + 10}{x ^{3}} d x

\int \frac{2 e ^{2 x}}{1 + e ^{4 x}} d x

\frac{d y}{d x} = 5 - 8 x

What is the limit as x approaches 0 of (8^x-14^x)/x ?
The limit as x approaches 0 of (8^x-14^x)/x is 3ln(2)-ln(14)