Bunuel wrote:

For integers x and y, 3^(4x+12) = 5^(3x+y). What is the value of y?

A. -12

B. -3

C. 0

D. 9

E. Cannot be determined

The key word in this question is INTEGERS

Notice that, if x is an integer, then 4x+12 is an integer, which means

3^(4x+12) will equal the product of a bunch of 3's Likewise, if x and y are integers, then 3x+y is an integer, which means

5^(3x+y) will equal the product of a bunch of 5's Given these conditions, it seems impossible that 3^(4x+12) could ever equal 5^(3x+y)

HOWEVER, if the exponents 4x+12 and 3x + y both equal ZERO, then we get 3^0 and 5^0, and both of these evaluate to equal 1 - PERFECT!

So, let 4x+12 = 0 and let 3x+y = 0

Now we'll solve this system of equations for x and y.

First, if 4x+12 = 0, then x = -3

If x = -3, then we can take 3x+y = 0 and replace x with -3 to get: 3(-3) + y = 0

Simplify: -9 + y = 0

Solve: y = 9

So, x = -3 and y = 9, is a solution to the equation 3^(4x+12) = 5^(3x+y)

Answer: D

Cheers,

Brent

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