Question 1209224: If 2x-3y = 5, then find (9^x)/(27^y) = ??
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Answer: 243
Work Shown
(9^x)/(27^y)
= ((3^2)^x)/((3^3)^y)
= (3^(2x))/(3^(3y))
= 3^(2x-3y)
= 3^(5)
= 243
We conclude that (9^x)/(27^y) = 243 when 2x-3y = 5.
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Another approach.
Pick any point on the line 2x-3y = 5.
Let's say we pick the point (x,y) = (4,1).
You can determine this point by looking at the graph, or do a bit of trial-and-error.
Note that 2x-3y = 2*4-3*1 = 8-3 = 5 which confirms (4,1) is on this line.
This ordered pair makes 2x-3y = 5 true.
(9^x)/(27^y)
= (9^4)/(27^1)
= (6561)/(27)
= 243
We arrive at the same answer.
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