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Popular >

limit as x approaches infinity+of (log_{4}(x))/(log_{7)(x)}

Solution

x \to \infty + lim (\frac{lo g _{4} ( x )}{lo g _{7} ( x )})

Solution

\frac{ln ( 7 )}{2 ln ( 2 )}

+1

Decimal Notation

1.40367 \dots

Solution steps

x \to \infty lim (\frac{lo g _{4} ( x )}{lo g _{7} ( x )})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{\frac{1}{2 l n ( 2 ) x}}{\frac{1}{x l n ( 7 )}})

= x \to \infty lim (\frac{\frac{1}{2 l n ( 2 ) x}}{\frac{1}{x l n ( 7 )}})

\frac{\frac{1}{2 l n ( 2 ) x}}{\frac{1}{x l n ( 7 )}} = \frac{ln ( 7 )}{2 ln ( 2 )}

= x \to \infty lim (\frac{ln ( 7 )}{2 ln ( 2 )})

x \to a lim c = c

= \frac{ln ( 7 )}{2 ln ( 2 )}

Popular Examples

limit as x approaches 4 of sqrt(x^2+20)

x \to 4 lim (x^{2} + 20)

derivative of (3x^2/(sqrt(x^2+2x-1)))

\frac{d}{d x} (\frac{3 x ^{2}}{x ^{2} + 2 x - 1})

tangent of f(x)=x^3-3x+1,\at x=2 tangent of

f (x) = x^{3} - 3 x + 1, at x = 2

integral of e^x-xe^x

\int e^{x} - x e^{x} d x

derivative of f(x)=-(42)/((x+4)^4)derivative of

f (x) = - \frac{42}{( x + 4 ) ^{4}}

Frequently Asked Questions (FAQ)

What is the limit as x approaches infinity+of (log_{4}(x))/(log_{7)(x)} ?
The limit as x approaches infinity+of (log_{4}(x))/(log_{7)(x)} is (ln(7))/(2ln(2))