How to solve 9^x-10*3^x-24=0
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How to solve 9^x-10*3^x-24=0

[From: ] [author: ] [Date: 11-10-29] [Hit: ]
I have a question for you. Are there any brackets involved?......
can some one help me isolate x i have been trying for hours now, and can't seem to get the right result :(

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9 = 3^2
9^x = (3^2)^x = 3^(2x) = (3^x)^2
(3^x)^2 - 10(3^x) - 24 = 0
Let u = 3^x
u^2 - 10u - 24 = 0.

(u - 12)(u + 2) = 0
3^x = 12 or 3^x = -2
x ln 3 = ln 12
x = ln 12/ln 3

3^x cannot equal -2 for any real x.

This problem is pretty filthy, and whoever assigned it to you is a dirty person for doing so.

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9^(x) - 10*3^(x) - 24 = 0

3^(2x) - 10*3^(x) - 24 = 0

(3^(x) - 12)(3^(x) + 2) = 0

3^(x) = 12 --> x = ln(12)/ln(3)

3^x = -2 .. Not possible

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Well first, I have a question for you. Are there any brackets involved?
1
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