# Log and nl stuff

• June 5th 2010, 07:17 PM
windia
Log and nl stuff
I keep on getting these wrong and I don't know what am I doing wrong for these problems:

1. 1/3ln3 + 2ln3
I first moved 1/3 and the equation becomes ln3^1/3 + ln3^2, after that I combined them and it becomes ln3^7/3. And that last step is where I was marked wrong.

2. ln20 - ln5 - 2/3ln8
I boiled down to ln4 - ln4 and after that I wrote 1 as final answer. It was marked wrong but I thought subtraction in ln means division?
• June 5th 2010, 07:36 PM
TheCoffeeMachine
Quote:

Originally Posted by windia
1. 1/3ln3 + 2ln3
I first moved 1/3 and the equation becomes ln3^1/3 + ln3^2, after that I combined them and it becomes ln3^7/3. And that last step is where I was marked wrong.

Correct. But perhaps you were required to write it in the form ${a}\ln{c}$?
Quote:

[2. ln20 - ln5 - 2/3ln8
I boiled down to ln4 - ln4 and after that I wrote 1 as final answer. It was marked wrong but I thought subtraction in ln means division?
That's right. But when you perform the division, you get $\ln\left(\dfrac{4}{4}\right) = \ln\left(1\right)$. Now, what's $\ln\left(1\right)$?
• June 5th 2010, 07:52 PM
windia
Ahh I see lol
• June 5th 2010, 11:47 PM
earboth
Quote:

Originally Posted by windia
I keep on getting these wrong and I don't know what am I doing wrong for these problems:

1. 1/3ln3 + 2ln3
I first moved 1/3 and the equation becomes ln3^1/3 + ln3^2, after that I combined them and it becomes ln3^7/3. And that last step is where I was marked wrong.

2. ln20 - ln5 - 2/3ln8
I boiled down to ln4 - ln4 and after that I wrote 1 as final answer. It was marked wrong but I thought subtraction in ln means division?

to #1: Your calculations seem to be OK, but your notation is horrible. Actually you should write the result as: ln(3^(7/3)).

to #2: This term is quite ambiguous. You have to use brackets to be clear:

(ln(20) - ln(5)) - 2/3ln(8) = $\ln\left(\dfrac{\frac{20}{5}}{4}\right) = \ln(1)=0
$

ln(20) - (ln(5) - 2/3ln(8)) = $\ln\left(\dfrac{20}{\frac54}\right)=\ln(16)$
• June 6th 2010, 12:58 AM
Drexel28
Quote:

Originally Posted by windia
I boiled down to ln4 - ln4 and after that I wrote 1 as final answer. It was marked wrong but I thought subtraction in ln means division?

Did you forget that $x-x=0$?