i cant seem to use any of the exponential rules. if the bases are not the same how can i get to x

3^x * 4^y = 177147 x - y = 11

Here is the best approach for this problem:


if x = 0, y = -11,

we'd have 1 * 4^(-11), which is a very small number



if x = 11, y = 0

we'd have 3^11 * 1, which seems reasonable, 3^11 could be 177147, so x = 11 is the best answer choice



if x = 177136, y = 177125

we'd have 3^177136 * 4^177125, which is much larger than 177147


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