## anonymous one year ago Help understanding exponent laws: I have an equation ln(x-y)=lnx+c. When I simplify a bit, I get 1-y=x+e^c, but the professor writes it as 1-y=cx. How is that possible?

1. anonymous

sorry typo.... ln(1-y)**

2. anonymous

ln(1-y)=lnx+c ..... somehow simplifies to 1-y=cx. I am getting 1-y=x+e^c

3. Empty

Well two things here, you can rewrite $c= \ln (e^c)$ and it will combine like this: $\ln(1-y)=\ln x+\ln e^c = \ln (e^c * x)$ $1-y = e^c x$ of course since $$e^c$$ is arbitrary, just making it your new constant doesn't matter.

4. Empty

If log rules make you uneasy, I suggest just doing it this way instead: $\ln( 1-y) = \ln x + c$ raise these as exponents: $e^{\ln(1-y)} = e^{\ln x + c}$ then you can separate out the exponents with exponent rules instead of log rules: $e^{\ln(1-y)} = e^{\ln x + c} = e^{\ln x }e^c$ And then you get the same answer

5. mathstudent55

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6. anonymous

Thank you everyone. I am a little shaky on the exponent laws so that was helpful.