Find-n-in-this-equation-2-n-4096-

Question Number 106630 by zahaku last updated on 06/Aug/20

F i n d n i n t h i s e q u a t i o n :

{(- 2)}^{n} = 4096

Answered by bemath last updated on 06/Aug/20

{(- 2)}^{n} = (1024) \times 4 = {(2)}^{12} = {(- 2)}^{12}

\to n = 12 . @ bemath @

Commented by zahaku last updated on 06/Aug/20

T h e r e {i s n}^{'} t a n o t h e r w a y t o f i n d n

i n t h e s a m e e q u a t i o n ?

Answered by Aziztisffola last updated on 06/Aug/20

n i s e v e n \Rightarrow n = 2 p

{(- 2)}^{n} = 4096 \Leftrightarrow {(- 2)}^{2 p} = 4096

\Leftrightarrow 4^{p} = 4096 \Rightarrow \ln (4^{p}) = \ln (4096)

\ln (4) p = \ln (4096) \Rightarrow p = \frac{\ln (4096)}{2 \ln (2)}

2 p = \frac{\ln (4096)}{\ln (2)} = 12

2 p = 12 = n \Rightarrow n = 12 .

Commented by zahaku last updated on 06/Aug/20

P l e a s e c a n y o u e x p l a i n h o w {(- 2)}^{2 p} b e c o m e s 4 p ?

Commented by Aziztisffola last updated on 06/Aug/20

{(- 2)}^{2 p} = {({(- 2)}^{2})}^{p} = 4^{p}

Commented by zahaku last updated on 06/Aug/20

T h a n k y o u .

Commented by Aziztisffola last updated on 06/Aug/20

{you}^{'} re welcome