differentiation of logs (1 Viewer)

Twiggyy

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heyy can any1 plz explain this for me
differentiate: y = log (base 2) x

thankuu
 

rama_v

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y = log2x
= logex/loge2 (change of base formula)

y' = (u'v - uv') / v2

where u = ln x
and v = ln 2

so y' = (1/x)(ln2) - (lnx)(0) / (ln 2)2
= (ln 2)/x[(ln2)2]
= 1/xln2

lol, I really do need to revise :p Read Trev's solution below
 
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Riviet

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What do you type to get the little subscript of e in logex?
 

Twiggyy

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thanxx

ohh ok i get wat u guys did after the change of base formula

but wat the hell do u do with the change of base formula i can never understand it

why did you put log of E?

and also i see sum questions that r the change of base rule.. except they dnt put log (base e) they put a number like log (base 4) or sumfin... how does that work???

lol sory but im reaaly freakin out bout this
 

Twiggyy

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to captain ghey - yeh i didnt no bout it either but i saw it in the 2001 catholic trials it was question 8
so yea i havnt seen it in the syllabus either but the stupid maths bos can chuck anything at us.
 

Dreamerish*~

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Twiggyy said:
ohh ok i get wat u guys did after the change of base formula

but wat the hell do u do with the change of base formula i can never understand it

why did you put log of E?

and also i see sum questions that r the change of base rule.. except they dnt put log (base e) they put a number like log (base 4) or sumfin... how does that work???

lol sory but im reaaly freakin out bout this
It depends on what you're trying to solve. There is no reason to use log4 (or any other base that's not 10 or e) if it doesn't help in solving an equation algebraically as only log10 and loge are on the calculator - loge is ln.

He used loge because you can differentiate it.
 

Twiggyy

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^^ ok so wen ur differentiating ... u use the change of base rule with log (base e) ??
 

Captain Gh3y

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Twiggyy said:
to captain ghey - yeh i didnt no bout it either but i saw it in the 2001 catholic trials it was question 8
so yea i havnt seen it in the syllabus either but the stupid maths bos can chuck anything at us.
In a catholic paper huh?
Ah, so there's 0 chance it would appear in the actual HSC then. That's good.
 

acmilan

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12.3 The functions y = ax and y = logax for a > 0 and real x. Change of base.
12.4 The derivatives of y = ax and y = logax. Natural logarithms and exponential function.

Yes, it's in the syllabus.
 

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