# Homework Help: Natrual log, solve for x

1. Jun 22, 2011

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

If (sinx)*(lnx)= 0 over [0, 2pi], then what does x equal?

Ok, I know I posted a question similar to this one a few days back, but I need some clarification on something. Below is the work that someone showed me.

lnx=sin^-1 (0)
lnx=0
Log$\hat{}x$$\check{}e$=0 (If you dont understand that, it is log and the superscript is x, subscript is e)
x=1

First of all, is that correct? Does x=1?

And if so, how did they get the sin inverse over to the right hand side of the equation, because you are not dividing it by 1, you are dividing it by 0, which would just make it 0, not sin inverse. Please clarify if you can. Thanks in advance.

2. Jun 22, 2011

### gb7nash

You're looking at this way too hard. You're multiplying two expressions together, so the only way you're going to get 0 is if sinx = 0 or lnx = 0.

For what value of x is sinx = 0 from [0, 2pi]? For what value of x is lnx = 0 from [0, 2pi]?

3. Jun 22, 2011

### SammyS

Staff Emeritus
Well, x=1 is one solution, but you're right, that is not the way to use the arcsin function.

To solve (sin(x))*(ln(x))= 0 over [0, 2pi], use the zero product property.