Simplify:
(15^x + 15^x+1) = (15^y)(4^y)
If we just take the left hand side of the equation:
(15^x + 15^x+1)
can be simplified to:
(15^x + 15^x(15^1))
I dont understand how we get to the next simplification. It is factored into the following:
15^x(1+15)
my brain is just giving up on me this evening after a long day at work ... so thanks in advance for your assistance !
Exponents: Simplify (15^x + 15^x+1) = (15^y)(4^y)
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(15^x + 15^x+1) = 15^y4^y
(15^x + 15^x+1)
can be simplified to:
(15^x + 15^x(15^1))
15^x(1+15) :Almost there
or 15^x(16) = 15^y4^y
or 15^x(4)^2 = 15^y4^y
Since both the sides are equal and both have same BASES so the powers MUST also be same. This means
y = 2
Hope it helps
Thanks
Komal
(15^x + 15^x+1)
can be simplified to:
(15^x + 15^x(15^1))
15^x(1+15) :Almost there
or 15^x(16) = 15^y4^y
or 15^x(4)^2 = 15^y4^y
Since both the sides are equal and both have same BASES so the powers MUST also be same. This means
y = 2
Hope it helps
Thanks
Komal
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- Location: Toronto
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15^x + 15^x(15^1)(15^x + 15^x(15^1))
I dont understand how we get to the next simplification. It is factored into the following:
15^x(1+15)
is the same as:
1(15^x) + 15(15^x)
which is the same as:
(1+15)(15^x)
and finally
16(15^x)
Here's another way to think about it:
15^x + 15^x(15^1)
is analagous to:
A + A(15)
which is 1A + 15A = 16A
When you have really complicated expressions on the GMAT and you're not sure what to do with them, asking what you'd do in simpler situations can often be a huge help; a fundamental rule of math is that no matter how wacky something looks, the same rules always apply.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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