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condense this to a single quantity: 1/2lnX +ln(x+3)-ln(x^2 +1) thanks.

Mathematics
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This appears to become a quadratic equation
really? well im not sure because its logarithms and u need to condense it.

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how did you get that?
well it is wrong, so don't write it!
i made a mistake
oh i see could you please explain it to me?
\[\frac{1}{2}\ln(x)=\ln(\sqrt{x})\]
because \[\ln(x^n)=n\ln(x)\]
here i am going from the right hand side to the left hand side.
\[\frac{1}{2}\ln(x)=\ln(x^{\frac{1}{2}})=\ln(\sqrt{x})\]
then we use \[\ln(ab) = \ln(a)+ln(b)\] again from the right to the left.
so we get \[\ln(\sqrt{x})+\ln(x+3)=\ln(\sqrt{x}(x+3))\]
then we use \[\ln(a)-\ln(b)=\ln(\frac{a}{b})\]
to get \[\ln(\sqrt{x}(x+3))-\ln(x^2+1)=\ln(\frac{\sqrt{x}(x+3)}{x^2+1})\]
i made a mistake on the first try and wrote \[\frac{1}{2}\ln(x)=\ln(x^2)\] which is wrong
there now i deleted it. hope the steps are clear
ohhh no i understand thanks so much!!:]
welcome!

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