a-x-m-log-a-m-x-So-is-following-true-i-2-1-log-i-1-2-

Question Number 58076 by Kunal12588 last updated on 17/Apr/19

a^{x} = m

\Rightarrow \log_{a} m = x

S o i s f o l l o w i n g t r u e

i^{2} = - 1

\log_{i} (- 1) = 2

Commented by $@ty@m last updated on 17/Apr/19

\log_{a} m = x i s d e f i n e d o n l y

f o r a (\neq 1) \in R

Answered by $@ty@m last updated on 17/Apr/19

Answered by MJS last updated on 17/Apr/19

\log_{i} (- 1) = \frac{\ln (- 1)}{\ln i}

e^{i π (2 m + 1)} = - 1 \Rightarrow \ln (- 1) = i π (2 m + 1)

e^{i π (2 n + \frac{1}{2})} = i \Rightarrow \ln i = i π (2 n + \frac{1}{2})

\Rightarrow \log_{i} (- 1) = \frac{4 m + 2}{4 n + 1} with m, n \in Z

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