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

Rohan Mcpherson

Answered question

2022-10-06

Calculating ln ( 1 + 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?

Answer & Explanation

oldgaffer1b

oldgaffer1b

Beginner2022-10-07Added 9 answers

The logarithm is not linear. That is, typically ln ( x + y ) ln ( x ) + ln ( y )
Janessa Benson

Janessa Benson

Beginner2022-10-08Added 1 answers

You are confusing your identities. You are most likely confusing the identity ln ( a b ) = ln a + ln b. In general ln ( a + b ) ln a + ln b. Also, note that if you are using a calculator, you do not need to simplify the expression; you can punch ln ( 1 + 3 ) straight into your calculator (but don't forget the brackets!).

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