Maths help - Logarithms (+REP)

[Matthew]

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

Oh and this is for C2 in case there are more advanced methods which you'd otherwise use .

[Kardan]

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]

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?

[Lee]

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]

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=zKV8Y...ure=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]

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=zKV8Y...ure=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]

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]

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.]

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.