OCR MEI AS core 2- June 2009

Hey guys if anyone out there can explain the answer to a question for me that would be great!

The question is Q9 ii. (June 2009 mei c2)

It is a logs question but ill have a go at typing it out:

(Loga^5+Loga^1/2)/Loga

So what i did was bring the powers to the front and did this

5Loga+0.5Loga-1Loga

then just did 5+0.5-1= 4.5

However looking at it I can see you just need to do (5+0.5)/1 :/

so my question is: why do we not need to use log rules to make the equation Loga5+Loga0.5-Loga? (that is what our teacher taught us!)

If i haven't explained very well please tell me

Because you have something that looks like (k log a) / log a which is just k (in this case k = 5.5)

You would use -log a if you had a term that said log(1/a) because 1/a is the same as a^-1, but you don't have that here - 1/loga is NOT the same as log(1/a).

ok thanks i understand!

i swear my teacher told us that subtracting logs is the same as dividing logs and dividing is the same as subtracting like this. loga-logb=loga/b

That's true, but as I tried to point out (perhaps not clearly) you have one log divided by another log, NOT the log of (one thing divided by another).