prove-that-log-1-3-3log-1-

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