Why Am I Getting Incorrect Solutions to This Logarithmic Substitution Problem?

[brandon1]

Homework Statement

(Idk how to put in the equation to make sense, therefore it is at the link below)

Homework Equations

The Attempt at a Solution

Here is all I have done. Something just isn't right...there should be 3 answers (in the back of the book) because there is a cube involved...

http://i123.photobucket.com/albums/o318/trashfile_bucket/Trash/2007-04-25-2009-26_edited.jpg

 

[mjsd]

note:
[tex](\log x)^3 \neq \log (x^3)[/tex] ie. 2nd step is wrong

hint: a make substitution: y = log x and solve for y first then x.

 

[Flux = Rad]

The first thing you've done is to cube both sides. That's ok but it should give you
[tex] ( log(x) )^3 = log(x) [/tex]
Since the whole log(x) is cubed, you can't move the 3 down (that's only if the x was cubed).

But what you can do is take all the terms over to one side and then you just have to solve a cubic (which will give you 3 solutions). You may want to make it easier to see by introducing a new variable, [tex] u = log(x) [/tex] for example.

 

[brandon1]

Good to go!

 

[sutupidmath]

and the solutiions should probbably be, couse i just glanced at it,:
x_1=1
x_2=y,(if the base of the logarithm is y, couse i could not see it clear)
x_3=1/y