Question 41300
I presume that your equation is {{{1/8=4^(5x-2)}}}.
This can be written as {{{2^-3=(2^2)^(5x-2)}}}
or {{{2^-3=2^(2(5x-2))}}}


Equating the index of 2 on both sides
-3 = 2(5x - 2)
or 10x = 4 - 3 = 1
or x = 1/10 =0.1


Answer is 0.1.


However if the equation is {{{1/8=4^(5x)-2}}} then
{{{1/8 + 2 =4^(5x)}}}
or {{{17/8 =(2^2)^(5x)}}}
or {{{17/8 =2^(2*5x)}}}
or {{{17 =2^(10x+3)}}} since {{{8=2^3}}}
Taking logarithm of both sides w.r.t. base 10
or log(17) = (10x+3)log(2)
or 10x + 3 = {{{log(17)/log(2)}}} = 4.087463
or 10x = 1.087463
or x = 0.1087463


Then the answer is 0.1087463.


Next time, before you put up a question make sure that there is no controversy about brackets.