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If 6^x-3[6^x-4]=1293*16^y, what is the value of x, in terms of y? (A)

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If 6^x-3[6^x-4]=1293*16^y, what is the value of x, in terms of y? (A) [#permalink]

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05 May 2017, 22:14
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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

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Re: If 6^x-3[6^x-4]=1293*16^y, what is the value of x, in terms of y? (A) [#permalink]

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05 May 2017, 23:53
ziyuen 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

Hi,

\begin{align*}
6^{x} - 3\times 6^{x-4} &= 1293 \times 36^{y} \\
6^{x-4}(6^{4} - 3) &= 1293 \times 36^{y}\\
6^{x-4}(1296 - 3) &= 1293 \times 6^{2y}\\
6^{x-4}\times 1293 &= 1293 \times 6^{2y}\\
\end{align*}

$$\Rightarrow x - 4 = 2y$$ or $$x = 2y+4$$

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If 6^x-3[6^x-4]=1293*16^y, what is the value of x, in terms of y? (A) [#permalink]

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06 May 2017, 00:06
$$6^x - \frac{3*6^x}{(6*6*6*6)} = 1293*36^y ====> 6^x -\frac{6^x}{(6*6*6*2)} = 1293*36^y ====> \frac{431*6^x}{(432*1293)} = 36^y ====> \frac{6^x}{(6^4)} = 36^y$$

Taking out the powers since they have common power as 36 = 6^2, we have

x-4 =2y
x = 2y+4(Option D)
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If 6^x-3[6^x-4]=1293*16^y, what is the value of x, in terms of y? (A)   [#permalink] 06 May 2017, 00:06
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