logs edexcel

Hi,
I’m not sure where I went wrong when combining all the Ln terms in this question.
In integration questions, I often do all the integration correctly but then I lose a mark because I combine the log terms incorrectly — so any general advice on how to stop doing this would be appreciated

I also looked at how BicenMaths simplified all the Ln for this question and he factored out the 2. I understand his method but I don’t understand why I got the wrong answer from what I did
thanks :smile:

Reply 1

Iqster

if it didn’t attach ^ (the M1 isn’t for the incorrect answer)

Reply 2

davros

Original post

by Iqster

if it didn’t attach ^ (the M1 isn’t for the incorrect answer)

when you had -ln(4) + ln(49) this is -ln(4/49) NOT -ln(4 x 49) :smile:

Reply 3

Iqster

Original post

by davros

when you had -ln(4) + ln(49) this is -ln(4/49) NOT -ln(4 x 49) :smile:

thank you! do you think i should group all the positive Ln terms first then?

Reply 4

tonyiptony

My personal preference is to simplify at the first instance. Here, I would simplify the ln expression in the first line, before plugging in 3 and 2, i.e. $\displaystyle 2\ln (|u|) - 2 \ln (|3+2u|) = \ln \frac{u^2}{(3+2u)^2}$ .
Please do fill in the details. Then plugging in the numbers would at least look less cumbersome.

I'd suppose you have a calculator for your exam? One way to check (and, in fact, to straight up get your answer) is to take exponential of your answer, using the fact that exp(ln(x)) = ln(exp(x)) = x (for positive x's).

Reply 5

mqb2766

Original post

by Iqster

thank you! do you think i should group all the positive Ln terms first then?

A slight alternative is to note that the limits are differenced when subbed (ln() arguments divided), so you can pretty much write down its
2 ln(3/2) - 2 ln(9/7) = 2 ln(7/6) = ln(49/36)
Leaving the two multiplier outside the ln() until the end means the argument numbers are smaller. Also, Id probably argue that 2 ln(7/6) is slightly simpler but Id expect either ans to be fine.

(edited 10 months ago)

Reply 6

Iqster

Original post

by tonyiptony

My personal preference is to simplify at the first instance. Here, I would simplify the ln expression in the first line, before plugging in 3 and 2, i.e. $\displaystyle 2\ln (|u|) - 2 \ln (|3+2u|) = \ln \frac{u^2}{(3+2u)^2}$ .
Please do fill in the details. Then plugging in the numbers would at least look less cumbersome.
I'd suppose you have a calculator for your exam? One way to check (and, in fact, to straight up get your answer) is to take exponential of your answer, using the fact that exp(ln(x)) = ln(exp(x)) = x (for positive x's).