What is the limit as x approaches 0 of (9^x-15^x)/x ?

The limit as x approaches 0 of (9^x-15^x)/x is 2ln(3)-ln(15)

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limit as x approaches 0 of (9^x-15^x)/x

x \to 0 lim (\frac{9 ^{x} - 1 5 ^{x}}{x})

2 ln (3) - ln (15)

Decimal Notation

- 0.51082 \dots

Solution steps

x \to 0 lim (\frac{9 ^{x} - 1 5 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{2 ln ( 3 ) \cdot 9 ^{x} - 1 5 ^{x} ln ( 15 )}{1})

= x \to 0 lim (\frac{2 ln ( 3 ) \cdot 9 ^{x} - 1 5 ^{x} ln ( 15 )}{1})

Plug in the value

x = 0

= \frac{2 ln ( 3 ) \cdot 9 ^{0} - 1 5 ^{0} ln ( 15 )}{1}

Simplify

\frac{2 ln ( 3 ) \cdot 9 ^{0} - 1 5 ^{0} ln ( 15 )}{1} : 2 ln (3) - ln (15)

= 2 ln (3) - ln (15)

\frac{d}{d x} (\frac{sin ( x )}{2 - cos ( x )})

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

y^{^{''}} - 8 y^{^{'}} + 17 = 0

U (x) = - 0.04 x^{2} + 240 x - 10000

\int_{0}^{3} e^{x} - x^{2} d x

What is the limit as x approaches 0 of (9^x-15^x)/x ?
The limit as x approaches 0 of (9^x-15^x)/x is 2ln(3)-ln(15)