<p>If 32^a+b = 16^a+2b, then a =
a) b
b) 2b
c) 3b
d) b + 2
e) b - 2</p>
<p>The answer is C. I tried reading the answer explanation, but it makes no sense whatsoever.</p>
<p>in order to solve the equation you have to put everything in the same base. That is, you have to find a common base between for 16 and 32. 2^4=16 and 2^5=32. So use a common base of 2
Now that you have the same base you can solve the equation so:</p>
<p>(2^5)^(a+b) = (2^4)^(a+2b)
Using the multiplication rule of indices multiply 5(a+b) = 5a+5b and on the other side of equation using the multiplication rule of indices 4(a +2b) = 4a + 8b </p>
<p>Therefore we have 2^5a+5b = 2^4a+8b
therefore we have 5a + 5b = 4a + 8b
5a-4a = 8b - 5b = 3b
therefore a = 3b</p>
<p>I hope this helps</p>
<p>Ah, thank you very much!</p>
<p>Here’s another way for students that have trouble with the algebra. Let’s pick a value for b, say b=3. Then the answer choices become</p>
<p>(A) 3
(B) 6
(C) 9
(D) 5
(E) 1</p>
<p>Note that I chose a value for b that makes all answer choices different. The question now becomes:</p>
<p>If 32^(a+3) = 16^(a+6), then a = </p>
<p>Now we can just check all the answer choices and use our calculator. (C) is the only choice where both sides of the equation come out the same.</p>
<p>32^12=16^15</p>