SOLUTION: Solve the equation by making the bases the same on each side of the equation 5^x=1/125

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the equation by making the bases the same on each side of the equation 5^x=1/125      Log On


   

Question 373931: Solve the equation by making the bases the same on each side of the equation
5^x=1/125
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
5%5Ex+=+1%2F125
5%5Ex+=+%28125%29%5E%28-1%29 Substitute 125+=+5%5E3
5%5Ex+=+%285%5E3%29%5E%28-1%29 Simplify.
5%5Ex+=+5%5E%28-3%29 The bases are equal, so the exponents are equal.
x+=+-3
Check:
5%5E%28-3%29+=+1%2F125
1%2F5%5E3+=+1%2F125 5%5E3+=+125 so...
1%2F125+=+1%2F125