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

The limit as x approaches infinity of (log_{2}(x))^2 is infinity

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limit as x approaches infinity of (log_{2}(x))^2

x \to \infty lim ((lo g_{2} (x))^{2})

\infty

Solution steps

x \to \infty lim ((lo g_{2} (x))^{2})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= (x \to \infty lim (lo g_{2} (x)))^{2}

Apply the common limit:

x \to \infty lim (lo g_{2} (x)) = \infty

= \infty^{2}

Apply Infinity Property:

\infty^{c} = \infty

= \infty

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