SOLUTION: solve for x: 2^(x+2) + 2^x =160 im not sure what to do, can someone help me??

Question 65918: solve for x: 2^(x+2) + 2^x =160
im not sure what to do, can someone help me??
Answer by uma(370) (Show Source): You can put this solution on YOUR website!
Given that 2^(x+2) + 2^x = 160
==> (2^x)*(2^2) + 2^x = 160 [ as x^(a + b) = x^a * x^b]
==> 2^x (2^2 + 1) = 160 [removing 2^x as common factor]
==> 2^x (4 + 1) = 160
==> 2^x(5) = 160
==> 2^x = 160/5 [dividing by 5 throughout]
==> 2^x = 32
==> 2^x = 2^5 [as 32 = 2^5]
as the bases are the same we equate the exponents.
==> x = 5

Good Luck!!!
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