# Homework Help: Log substitution problem

1. Apr 25, 2007

### brandon1

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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

2. Apr 25, 2007

### mjsd

note:
$$(\log x)^3 \neq \log (x^3)$$ ie. 2nd step is wrong

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

3. Apr 25, 2007

The first thing you've done is to cube both sides. That's ok but it should give you
$$( log(x) )^3 = log(x)$$
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, $$u = log(x)$$ for example.

4. Apr 25, 2007

### brandon1

Good to go!

5. Apr 27, 2007

### 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

Last edited: Apr 27, 2007