What is the limit as x approaches 0 of (7^x-6^x)/x ?

The limit as x approaches 0 of (7^x-6^x)/x is ln(7)-ln(6)

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limit as x approaches 0 of (7^x-6^x)/x

x \to 0 lim (\frac{7 ^{x} - 6 ^{x}}{x})

ln (7) - ln (6)

Decimal Notation

0.15415 \dots

Solution steps

x \to 0 lim (\frac{7 ^{x} - 6 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{7 ^{x} ln ( 7 ) - 6 ^{x} ln ( 6 )}{1})

= x \to 0 lim (\frac{7 ^{x} ln ( 7 ) - 6 ^{x} ln ( 6 )}{1})

Plug in the value

x = 0

= \frac{7 ^{0} ln ( 7 ) - 6 ^{0} ln ( 6 )}{1}

Simplify

\frac{7 ^{0} ln ( 7 ) - 6 ^{0} ln ( 6 )}{1} : ln (7) - ln (6)

= ln (7) - ln (6)

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

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

x \to - \infty lim (- 3 x^{5} + 2 x - 4)

x \to 3 lim (\frac{x ^{2} + 3}{x + 3})

x \to 1 lim (x^{l n (x)})

What is the limit as x approaches 0 of (7^x-6^x)/x ?
The limit as x approaches 0 of (7^x-6^x)/x is ln(7)-ln(6)