SOLUTION: Solve the equation for x. 125^x-2=25^3x+1

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Question 194280: Solve the equation for x.
125^x-2=25^3x+1
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
125%5E%28%28x-2%29%29+=+25%5E%28%283x%2B1%29%29 Substitute 125+=+5%5E3 and 25+=5%5E2
%285%5E%283%29%29%5E%28%28x-2%29%29+=+%285%5E2%29%5E%28%283x%2B1%29%29 Simplify.
5%5E%28%283x-6%29%29+=+5%5E%28%286x%2B2%29%29 The bases (5) are equal so the exponents are equal.
3x-6+=+6x%2B2 Subtract 3x from both sides.
-6+=+3x%2B2 Subtract 2 from both sides.
-8+=+3x Divide both sides by 3.
x+=+-8%2F3
Solution:
x = -2 2/3