Expert: Steve Holleran - 11/16/2007

Question
i cant seem to work this one out although it should be simple

2^x - 2^(x-2) = 3(2)^13

^ is exponent... i cant figure how to solve this quickly i think there may have been a typo... can you help?

Answer
Hi Adam,

Okay, lets try this:

on the left, break the 2^x into 2^(x-2) * 2^2:

then       2^(x-2) * 2^2 - 2^(x-2) = 3 * 2^13

factor out 2^(x-2) from the left side:

          2^(x-2) * [2^2 - 1] = 3 * 2^13

then       2^(x-2) * (4-1) = 3 * 2^13

and        2^(x-2) * 3  = 3 * 2^13

cancel the 3's:    2^(x-2) = 2^13

then              x-2 = 13 and x = 15.

Hope this is clear enough.

Steve