Thread: Help with simple equation needed.

Hi,

I cannot solve the following equation to x.



I tried it like this:



after some squaring and multiplying I got the following:



Then I didn't know how to continue. Wolfram Alpha says that x is 2/3: http://www.wolframalpha.com/input/?i=2-3x+%3D+%28lg%28243%29%2F%28lg%2827%29%29%29^2*%283 x-2%29

My textbook, from where I have this equation, also says x = 2/3. But I don't know how to get there. I hope that someone can post the last steps to solve to x.

Originally Posted by Antamara

Hi,

I cannot solve the following equation to x.



I tried it like this:



after some squaring and multiplying I got the following:



Then I didn't know how to continue. Wolfram Alpha says that x is 2/3: http://www.wolframalpha.com/input/?i=2-3x+%3D+%28lg%28243%29%2F%28lg%2827%29%29%29^2*%283 x-2%29

My textbook, from where I have this equation, also says x = 2/3. But I don't know how to get there. I hope that someone can post the last steps to solve to x.

Why didn't you try

?

Then equate the indices and square both of them

Do you "see" (from Archie's reply) that 3SQRT(2 - 3x) = 5SQRT(3x - 2) ?

Thank you very much for the fast answers. I tried it with Archie Meades' recommendation and it works. I also tried to continue from here:



I transformed the above equation to this:



Which gives x = 2/3.

Notice that, as Archie Meade pointed out, while . That means that .