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how could I have solved this?
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See attached picture. The OA is A. 2. . It involves a lot of clever manipulation. My question is how could I have been known to do these manipulations? Is there a shortcut or a cue that I don't know about? thanks
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DanaJ
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The fraction can be rewritten as:
15^x + 15^(x + 1) = (4^y) * (15^y)
Deal with the left side first:
15^x + 15^(x + 1) = (15^x) * (1 + 15) = (15^x) * 16 = (15^x) * (4^2)
So you have that:
(15^x)*(4^2) = (4^y)*(15^y) --- since 4^2 has to be equal to 4^y, you get y = 2. This means that:
(15^x)*(4^2) = (4^2)*(15^2) --- divide each side by 4^2 to get
15^x = 15^2 --- x = 2.
15^x + 15^(x + 1) = (4^y) * (15^y)
Deal with the left side first:
15^x + 15^(x + 1) = (15^x) * (1 + 15) = (15^x) * 16 = (15^x) * (4^2)
So you have that:
(15^x)*(4^2) = (4^y)*(15^y) --- since 4^2 has to be equal to 4^y, you get y = 2. This means that:
(15^x)*(4^2) = (4^2)*(15^2) --- divide each side by 4^2 to get
15^x = 15^2 --- x = 2.
