What is the limit as x approaches 0 of (3^x-7^x)/x ?

The limit as x approaches 0 of (3^x-7^x)/x is ln(3)-ln(7)

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limit as x approaches 0 of (3^x-7^x)/x

x \to 0 lim (\frac{3 ^{x} - 7 ^{x}}{x})

ln (3) - ln (7)

Decimal Notation

- 0.84729 \dots

Solution steps

x \to 0 lim (\frac{3 ^{x} - 7 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 ^{x} ln ( 3 ) - 7 ^{x} ln ( 7 )}{1})

= x \to 0 lim (\frac{3 ^{x} ln ( 3 ) - 7 ^{x} ln ( 7 )}{1})

Plug in the value

x = 0

= \frac{3 ^{0} ln ( 3 ) - 7 ^{0} ln ( 7 )}{1}

Simplify

\frac{3 ^{0} ln ( 3 ) - 7 ^{0} ln ( 7 )}{1} : ln (3) - ln (7)

= ln (3) - ln (7)

x \to 2 lim (3 x - 4 x^{2})

x \to 0 lim (ln (x) x^{2})

x \to 1 lim (\frac{2 x + 4}{x - 1})

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

x \to 1 lim (1 - 2 x)

What is the limit as x approaches 0 of (3^x-7^x)/x ?
The limit as x approaches 0 of (3^x-7^x)/x is ln(3)-ln(7)