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Exponents: Simplify (15^x + 15^x+1) = (15^y)(4^y)

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by II » Tue Feb 26, 2008 3:37 pm
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 !
Last edited by II on Mon May 05, 2008 2:21 am, edited 1 time in total.
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by joshi.komal » Tue Feb 26, 2008 4:18 pm
(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
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by Stuart@KaplanGMAT » Tue Feb 26, 2008 6:23 pm
(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)
15^x + 15^x(15^1)

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.
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by II » Wed Feb 27, 2008 12:48 am
Thanks guys ... that certainly makes a lot more sense !
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