# Domain with natural logs

• Jun 24th 2012, 02:40 PM
Domain with natural logs
I'm working with: $\displaystyle f(x)=ln(x)-ln(1-4x)$ and I need to figure out the domain of this function. I know that natural logs cannot be zero or negative numbers but is there a trick to simplying this to seeing the domain easily? Thanks.
• Jun 24th 2012, 02:47 PM
Reckoner
Re: Domain with natural logs
Quote:

I'm working with: $\displaystyle f(x)=ln(x)-ln(1-4x)$ and I need to figure out the domain of this function. I know that natural logs cannot be zero or negative numbers...

You said yourself that we cannot take the log of a nonpositive number. That means we must have $\displaystyle x > 0$ and $\displaystyle 1 - 4x > 0.$ Can you solve the second inequality for $\displaystyle x?$
• Jun 24th 2012, 02:51 PM
skeeter
Re: Domain with natural logs
Quote:

I'm working with: $\displaystyle f(x)=ln(x)-ln(1-4x)$ and I need to figure out the domain of this function. I know that natural logs cannot be zero or negative numbers but is there a trick to simplying this to seeing the domain easily? Thanks.
note that both $\displaystyle x > 0$ and $\displaystyle 1-4x > 0$
since $\displaystyle 1-4x > 0 \implies x < \frac{1}{4}$ , the intersection of these two restrictions is $\displaystyle 0 < x < \frac{1}{4}$ ... the domain.