1. ## Please solve equation

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

2. Yes, if you don't want to simplify further.

3. 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.

4. 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.

5. Originally Posted by oceanmd
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.
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