If-3-x-1-find-the-value-of-x-

Question Number 191203 by otchereabdullai last updated on 20/Apr/23

I f 3^{x} = - 1 f i n d t h e v a l u e o f x

Answered by Frix last updated on 20/Apr/23

3^{x} = - 1

e^{x \ln 3} = e^{i (2 n + 1) π}

x \ln 3 = i (2 n + 1) π

x = i \frac{(2 n + 1) π}{\ln 3}

Answered by Skabetix last updated on 20/Apr/23

3^{x} = i^{2}

x l n (3) = l n (i^{2})

x = \frac{l n (i^{2})}{l n (3)}

Commented by Skabetix last updated on 21/Apr/23

l n (i) = l n ({(- 1)}^{\frac{1}{2}}) = \frac{1}{2} l n (- 1) = \frac{1}{2} \times π i

s o l n (i^{2}) = 2 \times \frac{1}{2} \times π i = π i

Commented by Frix last updated on 21/Apr/23

The value of \ln (i^{2}) = ?

Answered by anr0h3 last updated on 21/Apr/23

- 1 = e^{i \cdot π}

3^{x} = e^{i \cdot π}

l n (3^{x}) = l n (e^{i \cdot π})

x \cdot l n (3) = i \cdot π

x = \frac{(\sqrt{- 1}) \cdot (π)}{l n (3)}

Commented by Frix last updated on 21/Apr/23

- 1 = e^{(2 n + 1) π i}

\ln (- 1) = (2 n + 1) π i

Complex logaritms are not unique

[why do you use \sqrt{- 1} instead of i at the end ?]

Commented by anr0h3 last updated on 21/Apr/23

that's correct, ln(-1) = ln(i^2) and ln(i^2)=(2n+1)πi