SOLUTION: Solve using logs:2^2x+4 minus 2^2x = 120 Please use steps God bless

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Question 133349: Solve using logs:2^2x+4 minus 2^2x = 120
Please use steps
God bless
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%282x%2B4%29-2%5E%282x%29+=+120 Start with the given equation


2%5E%282x%29%2A2%5E%284%29-2%5E%282x%29+=+120 Break up 2%5E%282x%2B4%29 using the identity x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez


2%5E%282x%29%282%5E%284%29-1%29+=+120 Factor out the GCF


2%5E%282x%29%2816-1%29+=+120 Evaluate 2%5E4 to get 16


2%5E%282x%29%2815%29+=+120 Subtract


2%5E%282x%29+=+8 Divide both sides by 15


2%5E%282x%29+=+2%5E3 Rewrite 8 as 2%5E3



Since the bases are equal, this means that the exponents are equal.


So

2x=3


x=3%2F2 Divide both sides by 2 to isolate x


So our answer is x=3%2F2 or x=1.5