What is the limit as x approaches 0 of (10^x-6^x)/x ?

The limit as x approaches 0 of (10^x-6^x)/x is ln(10)-ln(6)

Popular >

limit as x approaches 0 of (10^x-6^x)/x

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

ln (10) - ln (6)

Decimal

0.51082 \dots

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1 0 ^{x} ln ( 10 ) - 6 ^{x} ln ( 6 )}{1})

= x \to 0 lim (\frac{1 0 ^{x} ln ( 10 ) - 6 ^{x} ln ( 6 )}{1})

Plug in the value

x = 0

= \frac{1 0 ^{0} ln ( 10 ) - 6 ^{0} ln ( 6 )}{1}

Simplify

\frac{1 0 ^{0} ln ( 10 ) - 6 ^{0} ln ( 6 )}{1} : ln (10) - ln (6)

= ln (10) - ln (6)

a \to m lim (a x^{2} + b x + c)

x \to 7 lim (\frac{x - 7}{x - 4 - 3})

x \to - \infty lim (\frac{x}{x + 1} arctan (x))

x \to 0 lim (\frac{( ln ( 2 e + x ) - ln ( 2 e ) )}{x})

x \to 2 lim (a x^{2} + 2 x)

What is the limit as x approaches 0 of (10^x-6^x)/x ?
The limit as x approaches 0 of (10^x-6^x)/x is ln(10)-ln(6)