SOLUTION: 8x=2^(x-2) solve x

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Question 1191994: 8x=2^(x-2) solve x
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
8x = 2^(x-2) solve x
rewrite the 8 as a power of 2
2%5E3%2Ax+=+2%5E%28%28x-2%29%29
x = %282%5E%28x-2%29%29%2F%282%5E3%29
x = 2%5E%28x-2-3%29
x = 2%5E%28x-5%29
we know that x is a power of 2 greater than 5, x=8 is the obvious answer,

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


In general, this kind of equation, with one term a constant times the variable and another term with the variable in an exponent, can't be solved algebraically; you need to use a graphing calculator, or calculus or some other numerical method.

But this particular problem can be solved easily, because the answer is "nice".

We can tell that the equation will have a "nice" answer only if the value of the variable is an integer; if not, we would not be able to evaluate 2^(x-2) exactly.

So simply try small integer values for x to find the answer.
  x  x-2  8x  2^(x-2)
 --------------------
  3   1   24    2
  4   2   32    4
  5   3   40    8
  6   4   48   16
  7   5   56   32
  8   6   64   64

ANSWER: x=8