differentiation of logs (1 Viewer)

[Twiggyy]

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

thankuu

 

[rama_v]

y = log₂x
= log_ex/log_e2 (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 Read Trev's solution below

 

[Trev]

Since log_e2 is a constant you don't need to do what was done above.
y = (lnx)/(log_e2)
dy/dx = 1/(xlog_e2)

 

[DigitalFortress]

? isn't it just 1/x

 

[rama_v]

Yes, its just 1/x except with the 1/ln 2 pulled out the front
so its 1/xln2

 

[Riviet]

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

 

[Captain Gh3y]

Is the change of base formula (and differentiation of logs to base other than e) even in the syllabus? We never learnt it in class.

 

[Twiggyy]

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]

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*~]

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 log_e are on the calculator - log_e is ln.

He used log_e because you can differentiate it.

 

[Twiggyy]

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

 

[sunjet]

Trev is correct.

 

[Captain Gh3y]

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]

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

Yes, it's in the syllabus.