SOLUTION: aolvw for x:(1/125)^(4-2x)=5*25^(3x-1)

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Question 949350: aolvw for x:(1/125)^(4-2x)=5*25^(3x-1)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
(1/125)^(4-2x)=5*25^(3x-1)

1=(125)^(4-2x)*5*25^(3x-1)

5*(5^3)^(4-2x)*(5^2)^(3x-1)=1

5*5^(3(4-2x))*5^(2(3x-1))=1

The base is 5, and the factors raised to different exponents, all from the same base of 5.

Addition of those exponents: 1%2B3%284-2x%29%2B2%283x-1%29
1%2B12-6x%2B6x-2
13-2
11

Revising the equation,
highlight_green%28cross%285%5E11=1%29%29, which is false, so NO SOLUTION .



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The initial steps, rendered,

%281%2F125%29%5E%284-2x%29=5%2A25%5E%283x-1%29

1=%28125%29%5E%284-2x%29%2A5%2A25%5E%283x-1%29

5%2A%285%5E3%29%5E%284-2x%29%2A%285%5E2%29%5E%283x-1%29=1

5%2A5%5E%283%284-2x%29%29%2A5%5E%282%283x-1%29%29=1