Question

Log/Expo. Question... 8^x=1/2^(-3/x) Please help! :)

Answer 1

\[8^{x}=\frac{ 1 }{ 2^{^{-\frac{3 }{ x }}} }\]

Answer 2

Right side is the same as \(\large 2^{3/x}\).

Answer 3

is it like this one?
8^x=(1/2)^(-3/x)

Answer 4

And the left side is the same as \(\large 2^{3x}\) because 8=2^3.

Can you handle it from there, @suwhitney ?

Answer 5

Sorry, my computer is being slow.. im looking over everything

Answer 6

So I understand that that is what the right side is but then do I make it \[8=(2^{3})^{^{\frac{ 3 }{ x }}}\]??

Answer 7

use the left hand side as is as 8^x

Answer 8

I dont change it to 2^3?

Answer 9

8^x =8^1/x then whats next

Answer 10

x=1/x ?

Answer 11

well wouldnt it be x=3/x ?

Answer 12

x=1/x is correct.

Answer 13

Hint: This is a quadratic equation so will have two solutions.

Answer 14

1 and -1?

Answer 15

Those are the only two that work. It might be worthwhile to check both of those in the original equation to verify.

Answer 16

yeheeyyy ... :D you got it

Answer 17

Ok, thanks so much both of yall :)

Answer 18

Recap:

\[\large 8^x=\frac{1}{2^{-3/x}}\]
\[\large \rightarrow 2^{3x}=2^{3/x}\]
\[\large \rightarrow {3x}={3/x}\]
\[\large \rightarrow {x}={1/x}\]
\[\large \rightarrow x^2=1, \space x= \pm1\]

Answer 19

Thank you so much!! :)

Answer 20

You're welcome. Don't let these nasty-looking equations intimidate you. Break them down one step at a time!

Answer 21

I'll try not to :)