SAT Math Practice Exam

Category - Mathematics - Hard

If 82x-4= 42x, then x=
  1. 2
  2. 3
  3. 4
  4. 6
Explanation
Answer D- First change the base 8 and the base 4 to the same base 2.
8 = 23 and 4 = 22 Hence the equation can be written as
(23)2x-4 = (22)2x
26x-12 = 24x
6x-12 = 4x
2x = 12 or x =6

Key takeaway: When solving problems involving exponents, base is to be seen carefully. It is easy to simplify, as long as they have the same base. Remember following simple formulae:
am x an = am+n, am / an = a m-n , (am ) n = a m x n , (am ) 1/n = a m/ n
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