# Calculating ln(1+sqrt(3)) I distributed the natural logarithm and got (0+0.549) [placing the values in a calculator]. However, the answer key states that the answer is 1.0051.Where did I go wrong?

Rohan Mcpherson 2022-10-06 Answered
Calculating $\mathrm{ln}\left(1+\sqrt{3}\right)$
I distributed the natural logarithm and got $\left(0+0.549\right)$ [placing the values in a calculator]. However, the answer key states that the answer is $1.0051$
Where did I go wrong?
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oldgaffer1b
The logarithm is not linear. That is, typically $\mathrm{ln}\left(x+y\right)\ne \mathrm{ln}\left(x\right)+\mathrm{ln}\left(y\right)$
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Janessa Benson
You are confusing your identities. You are most likely confusing the identity $\mathrm{ln}\left(ab\right)=\mathrm{ln}a+\mathrm{ln}b$. In general $\mathrm{ln}\left(a+b\right)\ne \mathrm{ln}a+\mathrm{ln}b$. Also, note that if you are using a calculator, you do not need to simplify the expression; you can punch $\mathrm{ln}\left(1+\sqrt{3}\right)$ straight into your calculator (but don't forget the brackets!).