SOLUTION: solve the following equation for x: 27^(5-x) = 9^(x-2)

Question 567717: solve the following equation for x: 27^(5-x) = 9^(x-2)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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
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