Is the correct answer x = (5 ln 3 - 2 ln 4) : (ln 4-2 ln3)

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- Nov 15th 2007, 10:08 AMoceanmdPlease solve equation
Is the correct answer x = (5 ln 3 - 2 ln 4) : (ln 4-2 ln3)

- Nov 15th 2007, 10:35 AMticbol
Yes, if you don't want to simplify further.

- Nov 15th 2007, 11:40 AMoceanmd
How do you further simplify it? You mean to calculate on the calculator? Or is there another way? I am going to do it, I wanted to make sure that I solved it right. Thank you for your help.

- Nov 15th 2007, 11:41 AMoceanmd
How do you further simplify it? You mean to calculate on the calculator? Or is there another way? I am going to do it, I wanted to make sure that I solved it right. Thank you for your help.

- Nov 15th 2007, 02:07 PMticbol
4^(x +2) = 3^(2x +5)

(x +2)ln(4) = (2x +5)ln(3)

x*ln(4) +2ln(4) = 2x*ln(3) +5ln(3)

x[ln(4) -2ln(3)] = 5ln(3) -2ln(4)

x = [5ln(3) -2ln(4)] / [ln(4) -2ln(3)] ------your solution.

If you want to go on simplifying that, here is one way,

x = [ln(3^5) -ln(4^2)] / [ln(4) -ln(3^2)]

x = [ln(243) -ln(16)] / [ln(4) -ln(9)]

Since ln(a/b) = ln(a) -ln(b), then,

x = [ln(243/16)] / [ln(4/9)] --------------answer.

By calculator,

x = -3.354755646