What is the limit as x approaches 0 of (9^x-10^x)/x ?

The limit as x approaches 0 of (9^x-10^x)/x is 2ln(3)-ln(10)

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limit as x approaches 0 of (9^x-10^x)/x

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

2 ln (3) - ln (10)

Decimal Notation

- 0.10536 \dots

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{2 ln ( 3 ) \cdot 9 ^{x} - 1 0 ^{x} ln ( 10 )}{1})

= x \to 0 lim (\frac{2 ln ( 3 ) \cdot 9 ^{x} - 1 0 ^{x} ln ( 10 )}{1})

Plug in the value

x = 0

= \frac{2 ln ( 3 ) \cdot 9 ^{0} - 1 0 ^{0} ln ( 10 )}{1}

Simplify

\frac{2 ln ( 3 ) \cdot 9 ^{0} - 1 0 ^{0} ln ( 10 )}{1} : 2 ln (3) - ln (10)

= 2 ln (3) - ln (10)

z \to (1 - i) lim (x + i (2 x + y))

\frac{x}{x ^{2} + 16}

y = sin (x^{2})

\int \frac{- 6}{x ^{2} + 16} d x

What is the limit as x approaches 0 of (9^x-10^x)/x ?
The limit as x approaches 0 of (9^x-10^x)/x is 2ln(3)-ln(10)