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If 6^x−3[6^(x−4)]=1293(36^y), what is the value of x, in

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by Jay@ManhattanReview » Fri May 05, 2017 10:58 pm
ziyuenlau wrote:If 6^x−3[6^(x−4)]=1293(36^y), what is the value of x, in terms of y?

(A) y
(B) y+4
(C) y-4
(D) 2y+4
(E) 2y-4

Source : Math Revolution
OA=D
6^x-3[6^(x-4)]=1293(36^y)

= 2^x.3^x - 3.2^(x-4).3^(x-4) = 3.431.6^(2y)

= 2^x.3^x - 2^(x-4).3^(x-3) = 3^(2y+1).2^(2y).431

= 2^(x-4).3^(x-3).[2^4.3^3 - 1] = 3^(2y+1).2^(2y).431

= 2^(x-4).3^(x-3).431 = 3^(2y+1).2^(2y).431

= 2^(x-4).3^(x-3). = 3^(2y+1).2^(2y)

=> x-4 = 2y; equating the exponents of 2

=> x = 2y + 4

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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