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Popular >

limit as x approaches infinity+of (log_{6}(x))/(log_{8)(x)}

Solution

x \to \infty + lim (\frac{lo g _{6} ( x )}{lo g _{8} ( x )})

Solution

\frac{3 ln ( 2 )}{ln ( 6 )}

+1

Decimal Notation

1.16055 \dots

Solution steps

x \to \infty lim (\frac{lo g _{6} ( x )}{lo g _{8} ( x )})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{\frac{1}{x l n ( 6 )}}{\frac{1}{3 l n ( 2 ) x}})

= x \to \infty lim (\frac{\frac{1}{x l n ( 6 )}}{\frac{1}{3 l n ( 2 ) x}})

\frac{\frac{1}{x l n ( 6 )}}{\frac{1}{3 l n ( 2 ) x}} = \frac{3 ln ( 2 )}{ln ( 6 )}

= x \to \infty lim (\frac{3 ln ( 2 )}{ln ( 6 )})

x \to a lim c = c

= \frac{3 ln ( 2 )}{ln ( 6 )}

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Frequently Asked Questions (FAQ)

What is the limit as x approaches infinity+of (log_{6}(x))/(log_{8)(x)} ?
The limit as x approaches infinity+of (log_{6}(x))/(log_{8)(x)} is (3ln(2))/(ln(6))