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Math Help - Domain with natural logs

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    Domain with natural logs

    I'm working with: 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.
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    Re: Domain with natural logs

    Quote Originally Posted by Maskawisewin View Post
    I'm working with: 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 x > 0 and 1 - 4x > 0. Can you solve the second inequality for x?
    Thanks from Maskawisewin
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    Re: Domain with natural logs

    Quote Originally Posted by Maskawisewin View Post
    I'm working with: 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 x > 0 and 1-4x > 0

    since 1-4x > 0 \implies x < \frac{1}{4} , the intersection of these two restrictions is 0 < x < \frac{1}{4} ... the domain.
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