Question 683281

Please help me solve this question 
Evaluate: {{{8^(2(x+2))= 16^(x-2)}}}
I have started it but I'm not sure if I'm doing it right or how to continue.This is what I have:

log8^(2(x+2))=log16^(x-2)
2(x+2)log8= (x-2)log16
2xlog8 + 4log8 = xlog16 - 2log16
2xlog8 - xlog16 = -4log8 - 2log16

I don't know how to continue from here, can you please help me complete it, and tell me how you got from one step to the next. Thank you.


Convert to a similar base, which in this case is:  base 2


{{{8^(2(x+2))= 16^(x-2)}}}


{{{(2^3)^(2(x+2))= (2^4)^(x-2)}}}


{{{2^(6(x+2))= 2^(4(x-2))}}}


With bases being similar, exponents are too. Therefore, 6(x + 2) = 4(x - 2)


6x + 12 = 4x - 8


6x - 4x = - 8 - 12


2x = - 20


{{{x = (- 20)/2}}}, or {{{highlight_green(- 10)}}}


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