Question 1191994
<br>
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.<br>
But this particular problem can be solved easily, because the answer is "nice".<br>
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.<br>
So simply try small integer values for x to find the answer.<br><pre>
  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</pre>
ANSWER: x=8<br>