SOLUTION: I am getting stuck on this one: 1/8=4^5x-2 Please Help

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Question 41300: I am getting stuck on this one:
1/8=4^5x-2
Please Help
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
I presume that your equation is 1%2F8=4%5E%285x-2%29.
This can be written as 2%5E-3=%282%5E2%29%5E%285x-2%29
or 2%5E-3=2%5E%282%285x-2%29%29

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%2F8=4%5E%285x%29-2 then
1%2F8+%2B+2+=4%5E%285x%29
or 17%2F8+=%282%5E2%29%5E%285x%29
or 17%2F8+=2%5E%282%2A5x%29
or 17+=2%5E%2810x%2B3%29 since 8=2%5E3
Taking logarithm of both sides w.r.t. base 10
or log(17) = (10x+3)log(2)
or 10x + 3 = log%2817%29%2Flog%282%29 = 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.