Question 949350
(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+3(4-2x)+2(3x-1)}}}
{{{1+12-6x+6x-2}}}
{{{13-2}}}
{{{11}}}


Revising the equation,
{{{highlight_green(cross(5^11=1))}}}, which is false, so NO SOLUTION .




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The initial steps, rendered,


{{{(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}}}