prove that log(−1)^3 =3log(−1) ?


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Question Number 127363 by mohammad17 last updated on 29/Dec/20

$p r o v e t h a t l o g {(- 1)}^{3} = 3 l o g (- 1) ?$
Commented by mohammad17 last updated on 29/Dec/20

$? ? ? ? ?$
Commented by mr W last updated on 29/Dec/20

$i n C w e h a v e a l w a y s$ $\log a^{b} = b \log a$
Commented by mohammad17 last updated on 29/Dec/20

$Y e s, m y t e c h e r, b u t o u r d o c t o r w a n t s t o$ $p r o v e i t i n s t e p s$
	Answered by ebi last updated on 29/Dec/20

	$l e t s a y :$ $z = l o g (- 1)$ $(- 1) = e^{z} - - - t a k e e x p o n e n t o n b o t h s i d e$ ${(- 1)}^{3} = {(e^{z})}^{3} - - - t a k e p o w e r 3 o n b o t h s i d e$ ${(- 1)}^{3} = e^{3 z}$ $l o g {(- 1)}^{3} = 3 z - - - t a k e l o g o n b o t h s i d e$ $l o g {(- 1)}^{3} = 3 l o g (- 1) - - - s u b s t i t u t e z = l o g (- 1)$ $- - - G e n e r a l i z e - - -$ $m = {l o g}_{a} (x)$ $x = a^{m} - - - c o n v e r t t o e x p o n e n t i a l f o r m$ $x^{n} = {(a^{m})}^{n} - - - t a k e p o w e r n o n b o t h s i d e$ $x^{n} = a^{m n}$ ${l o g}_{a} {(x)}^{n} = m n - - - c o n v e r t t o l o g a r i t h m f o r m$ ${l o g}_{a} {(x)}^{n} = n {l o g}_{a} (x) - - - s u b s t i t u t e m = {l o g}_{a} (x)$
	Commented by mr W last updated on 29/Dec/20

	$z = l o g (- 1) \neq l o g (i)$
	Commented by mohammad17 last updated on 29/Dec/20

	$c a n y o u g i v e m e s t e b s$
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