What is the limit as x approaches infinity of ((6x))/(5log_{2)(x)} ?

The limit as x approaches infinity of ((6x))/(5log_{2)(x)} is infinity

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limit as x approaches infinity of ((6x))/(5log_{2)(x)}

x \to \infty lim (\frac{( 6 x )}{5 lo g _{2} ( x )})

\infty

Solution steps

x \to \infty lim (\frac{6 x}{5 lo g _{2} ( x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{6}{5} \cdot x \to \infty lim (\frac{x}{lo g _{2} ( x )})

Apply L'Hopital's Rule

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

= \frac{6}{5} \cdot x \to \infty lim (\frac{1}{\frac{1}{x l n ( 2 )}})

Simplify

= \frac{6}{5} \cdot x \to \infty lim (ln (2) x)

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{6}{5} ln (2) \cdot x \to \infty lim (x)

Apply the common limit:

x \to \infty lim (x) = \infty

= \frac{6}{5} ln (2) \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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What is the limit as x approaches infinity of ((6x))/(5log_{2)(x)} ?
The limit as x approaches infinity of ((6x))/(5log_{2)(x)} is infinity