Question 1199909: Find the pair of integers (a,b) for which 2^a+1 + 2^a = 3^b+2 - 3^b Found 3 solutions by greenestamps, MathTherapy, math_tutor2020:Answer by greenestamps(13195) (Show Source):
Surely the equation as you show it is not correct; it has an infinite number of solutions.
2^a+1 + 2^a = 3^b+2 - 3^b ==>
SOLUTIONS: a=-1; b is any number
If you are working on a problem like this, your level of knowledge of math should be enough for you to know that proper use of parentheses is important.
Assuming the equation I have solved above is NOT the equation you intended, re-post the problem correctly....
Find the pair of integers (a,b) for which 2^a+1 + 2^a = 3^b+2 - 3^b
If this is , then it SIMPLIFIES to the equation ,
and the integer-values for (a, b) = (3, 1).
You can put this solution on YOUR website!
I'm assuming the equation is
which is equivalent to writing out 2^(a+1)+2^a = 3^(b+2)-3^b
Use parenthesis for the exponents "a+1" and "b+2"
If my initial assumption is correct, then,
Use the rule a^(b+c) = a^b*a^c
Because the bases are different, the two sides are only equal when the exponents are zero (to make both sides to simplify to 1).
a-3 = 0 leads to a = 3
b-1 = 0 leads to b = 1
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