What is the limit as x approaches 0 of ((6^x-8^x))/x ?

The limit as x approaches 0 of ((6^x-8^x))/x is ln(6)-3ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 0 of ((6^x-8^x))/x

x \to 0 lim (\frac{( 6 ^{x} - 8 ^{x} )}{x})

ln (6) - 3 ln (2)

Decimal

- 0.28768 \dots

Solution steps

x \to 0 lim (\frac{6 ^{x} - 8 ^{x}}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{6 ^{x} ln ( 6 ) - 3 ln ( 2 ) \cdot 8 ^{x}}{1})

Plug in the value

x = 0

= \frac{6 ^{0} ln ( 6 ) - 3 ln ( 2 ) \cdot 8 ^{0}}{1}

Simplify

\frac{6 ^{0} ln ( 6 ) - 3 ln ( 2 ) \cdot 8 ^{0}}{1} : ln (6) - 3 ln (2)

= ln (6) - 3 ln (2)

What is the limit as x approaches 0 of ((6^x-8^x))/x ?
The limit as x approaches 0 of ((6^x-8^x))/x is ln(6)-3ln(2)