SOLUTION: 4^3x-2^3x= 20 what is the value of x

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Question 356236: 4^3x-2^3x= 20 what is the value of x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%283x%29-2%5E%283x%29=+20+
%282%5E2%29%5E%283x%29-2%5E%283x%29=20
2%5E%286x%29-2%5E%283x%29-20=0
Use a substitution, let u=2%5E%283x%29, then u%5E2=2%5E%286x%29
u%5E2-u-20=0
%28u-5%29%28u%2B4%29=0
Two solutions in u:
u-5=0
u=5
2%5E%283x%29=5
3x=log%282%2C%285%29%29
x=%281%2F3%29log%282%2C%285%29%29
x=%281%2F3%29%28log%28%285%29%29%2Flog%28%282%29%29%29
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u%2B4=0
u=-4
2%5E%283x%29=-4
No power of 2 will give a negative answer.
No solution from this u value.
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x=%281%2F3%29%28log%28%285%29%29%2Flog%28%282%29%29%29