SOLUTION: please help me solve this problem... 4^x=(1/2)^3x+5

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Question 255363: please help me solve this problem... 4^x=(1/2)^3x+5
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
If you mean
4%5Ex=%281%2F2%29%5E%283x%29%2B5, then
simplify as
4%5Ex+=+%281%2F8%29%5Ex+%2B+5.
multiplying both sides by 8^x, we get
32%5Ex+=+x+%2B+5%2A8%5Ex
in this case, there is no x value which is true.
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If you mean
4%5Ex=%28%281%2F2%29%5E3%29x%2B5
simplifies as
4%5Ex=%281%2F8%29x%2B5.
Multiply both sides by 8 to get
8%2A4%5Ex=x%2B5
In this case, there is no x value which is true.
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If you mean
4%5Ex=%281%2F2%29%5E%283x%2B5%29
then rewrite the right side as
4%5Ex+=+2%5E%28-3x-5%29
the 4 can be expressed as 2^2, so we get
2%5E%282x%29+=+2%5E%28-3x-5%29
cancel the base 2's to get
2x+=+-3x-5
solve for x to get
x+=+-1