SOLUTION: If 2 to the power of a times 2 to the power of b = 128, where a and b are consecutive positive integers and a < b, what is the value of a ?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: If 2 to the power of a times 2 to the power of b = 128, where a and b are consecutive positive integers and a < b, what is the value of a ?       Log On


   

Question 198999: If 2 to the power of a times 2 to the power of b = 128, where a and b are consecutive positive integers and a < b, what is the value of
a ?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
If %282%5Ea%29%2A%282%5Eb%29+=+128 and b+=+a%2B1 (a and b are consecutive positive integers.), then, substitute b = a+1...
%282%5Ea%29%282%5E%28a%2B1%29%29+=+128 Add the exponents on the left side.
2%5E%28%282a%2B1%29%29+=+128 but 128+=+2%5E7 so substitute...
2%5E%28%282a%2B1%29%29+=+2%5E7 The bases (2) are equal so the exponents must be equal.
2a%2B1+=+7 Subtract 1 from both sides.
2a+=+6 Divide both sides by 2.
highlight%28a+=+3%29