SOLUTION: (2^(x+1))=(2^(x-1))+48

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: (2^(x+1))=(2^(x-1))+48      Log On


   

Question 841736: (2^(x+1))=(2^(x-1))+48
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
A rule about exponents: b%5E%28a%2Bc%29=%28b%5Ea%29%2A%28b%5Ec%29.

See that in your equation you have a term 2%5E%28x%2B1%29, and you can do this:
2%5E%28x%2B1%29=%282%5E%28x-1%29%29%282%5E2%29.

Some steps........
%282%5E%28x%2B1%29%29=%282%5E%28x-1%29%29%2B48
2%5E%28x%2B1%29-2%5E%28x-1%29=48
%282%5E%28x-1%29%29%282%5E2-1%29=48
%282%5E%28x-1%29%29%284-1%29=48
%282%5E%28x-1%29%29%2A3=48 and then factor 48
3%2A2%5E%28x-1%29=3%2A2%5E4
2%5E%28x-1%29=2%5E4, the bases are the same, so the exponents must be equal.
-
x-1=4
x=4%2B1
highlight%28x=5%29