SOLUTION: Ooops I made a mistake the problem shows {{{32^x}}}={{{1/8}}} then x= I don't even understand this question so if someone can explain it to me all the step i would really apprecia

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Ooops I made a mistake the problem shows {{{32^x}}}={{{1/8}}} then x= I don't even understand this question so if someone can explain it to me all the step i would really apprecia      Log On


   

Question 21112: Ooops I made a mistake the problem shows 32%5Ex=1%2F8 then x= I don't even understand this question so if someone can explain it to me all the step i would really appreciate it thank you.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The question is: To what power (that's x) should 32 be raised to equal 1/8?
You can use logarithms to solve this.
32%5Ex+=+1%2F8 Take the log of both sides.
xlog32+=+log%281%2F8%29 Divide both sides by log32
x+=+%28log%281%2F8%29%29%2Flog32 Use your calculator to find the logarithms.
x+=+-0.6
Check:
32%5E%28-0.6%29+=+0.125
0.125+=+1%2F8
If you not into logarithms yet, try this:
32%5Ex+=+1%2F8 Now 32+=+2%5E5 and 1%2F8+=+2%5E%28-3%29
So you can write:
2%5E%285x%29+=+2%5E%28-3%29 Since the bases (2) are equal, the exponents must be equal.
So we have:
5x+=+-3 Divide both sides by 5.
x+=+-3%2F5
x+=+-0.6