What is the limit as x approaches 9 of (log_{3}(x)^2-4)/(log_{3)(x)-2} ?

The limit as x approaches 9 of (log_{3}(x)^2-4)/(log_{3)(x)-2} is 4

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limit as x approaches 9 of (log_{3}(x)^2-4)/(log_{3)(x)-2}

x \to 9 lim (\frac{lo g _{3} ( x ) ^{2} - 4}{lo g _{3} ( x ) - 2})

4

Solution steps

x \to 9 lim (\frac{lo g _{3} ( x ) ^{2} - 4}{lo g _{3} ( x ) - 2})

Simplify

\frac{lo g _{3} ( x ) ^{2} - 4}{lo g _{3} ( x ) - 2} : lo g_{3} (x) + 2

= x \to 9 lim (lo g_{3} (x) + 2)

Plug in the value

x = 9

= lo g_{3} (9) + 2

Simplify

lo g_{3} (9) + 2 : 4

= 4

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