SOLUTION: please solve and show me procedure, solve for x: 5^-1 =x^-6

Algebra ->  Equations -> SOLUTION: please solve and show me procedure, solve for x: 5^-1 =x^-6       Log On


   

Question 886824: please solve and show me procedure, solve for x: 5^-1 =x^-6
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
5%5E%28-1%29%22%22=%22%22x%5E%28-6%29

Move the factors with negative exponents to 
denominators with positive exponents:

1%2F5%5E1%29%22%22=%22%221%2Fx%5E6%29

1%2F5%5E1%29%22%22=%22%221%2Fx%5E6%29

Erase the 1 exponent:

1%2F5%29%22%22=%22%221%2Fx%5E6%29

Cross-multiply:

x%5E6%22%22=%22%225

Take sixth roots of both sides, remembering ±
on the right side:

root%286%2Cx%5E6%29%22%22=%22%22%22%22+%2B-+root%286%2C5%29

x%22%22=%22%22%22%22+%2B-+root%286%2C5%29

Edwin

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

please solve and show me procedure, solve for x: 5^-1 =x^-6 


x%5E-6+=+5%5E-1

log+%28x%5E-+6%29+=+log+%285%5E-+1%29 ------ Taking logs of both sides

-+6%28log+x%29+=+-+1%28log+5%29

log+x+=+%28%28-+1%29%2F-+6%29%28log+5%29

log+x+=+%281%2F6%29%28log+5%29

log+x+=+log+5%5E%281%2F6%29

Thus, x+=+5%5E%281%2F6%29, or highlight_green%28highlight_green%28x+=+1.307660486%29%29