Solve for x: 4^(x+2)=6^(2x-9)
[From: ] [author: ] [Date: 13-02-28] [Hit: ]
386x + 2.773 = 3.584x - 16.12618.899 = 2.198x8.......
Had you not supplied us with alternatives, then I would have written
Log(4^(x+2)) = Log(6^(2x-9))
(x + 2)Log(4) = (2x - 9)Log(6)
xLog(4) + 2Log(4) = 2xLog(6) - 9Log(6)
2Log(4) + 9Log(6) = 2xLog(6) - xLog(4) = x(2Log(6) - Log(4)) = xLog(36/4) = xLog(9)
So x = (2Log(4) + 9Log(6))/ Log(9) = Log(16×6^9)/Log(9) = 8.6010…
GL!
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Take the natural log of both sides, to take the variables out of the exponent.
(x+2)ln(4) = (2x-9)ln(6)
1.386x + 2.773 = 3.584x - 16.126
18.899 = 2.198x
8.598 = x
The answer is a
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It should be fairly simple.
(x+2) ln 4 = (2x-9) ln 6
x ln 4 + 2 ln 4 = 2x ln 6 - 9 ln 6
x ln 4 + 4 ln 2 = 2x ln 6 - 9 ln 6
x ln 4 - 2x ln 6 = - 4 ln 2 - 9 ln 6
2x ln 2 - 2x ln 6 = - 4 ln 2 - 9 ln 6
2x (ln 2 - ln 6) = - 4 ln 2 - 9 ln 6
x = (-2 ln 2 - 9/2 ln 6) / (ln 2 - ln 6) = 8.6 approximately
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Take the logarithms of both sides. It becomes very straightforward at that point. If you're in precalc, there should be a chapter on it. If you're in calculus, it should be covered in an appendix.
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A is the answer. What you do is plug in A for X and do the math. I wish you luck as i'm in algebra 1 and whatever your in you'll need the luck.
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4^(x + 2) = 6^(2x - 9)
(x + 2) log 4 = (2x – 9)log 6
(x + 2) × 1.3863 = (2x – 9) × 1.7918
1.3863x + 2.7726 = 3.5836x – 16.1262
2.1973x = 18.8988
x = 8.6
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Well if you plug in each number you can usually find the answer pretty quickly. Except none of those answers work if you plug them in. I think it's no solution.
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Take log with base 6 on both sides
x=2log_6(4) +9
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2 - log_6(4)
so answer is (a).
