View Full Version : Maths help - Logarithms (+REP)
Matthew
22-10-2012, 04:46 PM
I'm stuck on the following question:
Express log2(x+2) - log2x as a single logarithm.
Hence solve the equation log2(x+2) - log2x = 3.
I can do part "a"- log2(x+2) - log2x = log2(x+2)/x
But how do I do part "b"?
Its probably so easy haha but anyway, +REP for any help :D
Oh and this is for C2 in case there are more advanced methods which you'd otherwise use :).
Kardan
22-10-2012, 05:57 PM
Okay, so we have:
log2((x+2)/x) = log((x+2)/x)/log(2) = 3
Multiply both sides by log(2);
log((x+2)/x) = 3log(2)
Take the exponential of both sides;
(x+2)/x = 8
Rearrange for x;
-7x = -2
x = 2/7
Matthew
22-10-2012, 06:34 PM
Okay, so we have:
log2((x+2)/x) = log((x+2)/x)/log(2) = 3
Multiply both sides by log(2);
log((x+2)/x) = 3log(2)
Take the exponential of both sides;
(x+2)/x = 8
Rearrange for x;
-7x = -2
x = 2/7
Oh right, I didn't realise that log2 (x) = log (x)/log2.
Do you know if that is a C2 concept? I've missed one lesson recently so maybe I missed that, although I can't see anything in the text book about it :S
If it isn't C2, do you know a way that uses a C2 method?
Oh right, I didn't realise that log2 (x) = log (x)/log2.
Do you know if that is a C2 concept? I've missed one lesson recently so maybe I missed that, although I can't see anything in the text book about it :S
If it isn't C2, do you know a way that uses a C2 method?
Im sure I told you that in Mod Spam? :S
Kardan
22-10-2012, 06:39 PM
Oh right, I didn't realise that log2 (x) = log (x)/log2.
Do you know if that is a C2 concept? I've missed one lesson recently so maybe I missed that, although I can't see anything in the text book about it :S
If it isn't C2, do you know a way that uses a C2 method?
This video suggests it is a C2 Method
http://www.youtube.com/watch?v=zKV8YBvu_9o&list=PL35B157DCDB77C4DF&index=16&feature=plpp_video
Plus I can't think of any other methods that involve changing the base, and you will have to change the base in order to solve the equation.
Matthew
22-10-2012, 06:39 PM
Im sure I told you that in Mod Spam? :S
Eh?
In mod spam you said the following:
"Ouch" and (along the lines of) "No I can't do it"
haha
EDIT:
This video suggests it is a C2 Method
http://www.youtube.com/watch?v=zKV8YBvu_9o&list=PL35B157DCDB77C4DF&index=16&feature=plpp_video
Plus I can't think of any other methods that involve changing the base, and you will have to change the base in order to solve the equation.
Right, thanks for your help :)
LoveToStack
23-10-2012, 09:58 AM
log2((x+2)/x) = log((x+2)/x)/log(2) = 3
Out of curiosity, why did you bother changing the base? Why not just go:
log2(x+2 / x) = 3
x+2 / x = 23
In one step?
Kardan
23-10-2012, 10:42 AM
Out of curiosity, why did you bother changing the base? Why not just go:
log2(x+2 / x) = 3
x+2 / x = 23
In one step?
Just to show how to convert bases using the base conversion formula in C2.
Wig44.
23-10-2012, 08:02 PM
Out of curiosity, why did you bother changing the base? Why not just go:
log2(x+2 / x) = 3
x+2 / x = 23
In one step?
I'd advise this method. Change of base is a C2 method but you don't need it here.
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