SOLUTION: solve the following equation for x: 27^(5-x) = 9^(x-2)
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Question 567717
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solve the following equation for x: 27^(5-x) = 9^(x-2)
Answer by
jim_thompson5910(35256)
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27^(5-x) = 9^(x-2)
(3^3)^(5-x) = (3^2)^(x-2)
3^(3(5-x)) = 3^(2(x-2))
Since the bases are equal, the exponents are equal.
3(5-x)=2(x-2)
15-3x=2x-4
-3x=2x-4-15
-3x-2x=-4-15
-5x=-4-15
-5x=-19
x=(-19)/(-5)
x=19/5