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Popular >

limit as x approaches infinity of (log_{4}(x))/(log_{9)(x)}

Solution

x \to \infty lim (\frac{lo g _{4} ( x )}{lo g _{9} ( x )})

Solution

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

+1

Decimal

1.58496 \dots

Solution steps

x \to \infty lim (\frac{lo g _{4} ( x )}{lo g _{9} ( x )})

Apply L'Hopital's Rule

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

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

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

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

x \to a lim c = c

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

Graph

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Frequently Asked Questions (FAQ)

What is the limit as x approaches infinity of (log_{4}(x))/(log_{9)(x)} ?
The limit as x approaches infinity of (log_{4}(x))/(log_{9)(x)} is (ln(3))/(ln(2))