Question

Solve the following system: 2^(x+3y) = 128 and 2^(3x–y) = 2

Answer 1

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Answer 2

Apply log.

Answer 3

128 = 2^7
So,
2^(x+3y) = 128
2^(x+3y) = 2^7
Since the bases on both sides are the same, you can equate the power
x+3y = 7 <- This is equation 1

2^(3x–y) = 2
2^(3x–y) = 2^1
Since the bases on both sides are the same, you can equate the power
3x-y = 1 <- this is equation 2

You have two equations and two unknowns. You can solve them now.