What is the limit as x approaches-2 of log_{a}(x) ?

The limit as x approaches-2 of log_{a}(x) is (ln(2))/(ln(a))+i pi/(ln(a))

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limit as x approaches-2 of log_{a}(x)

x \to - 2 lim (lo g_{a} (x))

\frac{ln ( 2 )}{ln ( a )} + i \frac{π}{ln ( a )}

Solution steps

x \to - 2 lim (lo g_{a} (x))

Apply the common limit:

x \to - 2 lim (lo g_{a} (x)) = \frac{ln ( 2 ) + iπ}{ln ( a )}

= \frac{ln ( 2 ) + iπ}{ln ( a )}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{ln ( 2 ) + iπ}{ln ( a )} = \frac{ln ( 2 )}{ln ( a )} + \frac{iπ}{ln ( a )}

= \frac{ln ( 2 )}{ln ( a )} + i \frac{π}{ln ( a )}

\int \frac{1 - 3 y}{2 y - 3 y ^{2}} d y

\frac{d}{d x} (lo g_{2} (1 - 3 x))

(- 6 x^{5} + 12)^{4}

\frac{x ^{2}}{x + 3}

n = 0 \sum \infty 9 + 3 + 1

What is the limit as x approaches-2 of log_{a}(x) ?
The limit as x approaches-2 of log_{a}(x) is (ln(2))/(ln(a))+i pi/(ln(a))