Is the derivative of f(x) = log(base 5) x equal to 1/(x * ln(5))?

[courtrigrad]

Hello all

I was just wondering whether this is acceptable:

f(x) = log (base 5) x.

f' '(x) = 1 / x * log (base 5) e.

Any responses are greatly appreciated!

 

[Zurtex]

Well I don't actually see a method here, try and work it out:

$$y= \log_a (x)$$

$$a^y = x$$

$$\ln (a) a^y \frac{dy}{dx} = 1$$

$$\frac{dy}{dx} = \frac{1}{\ln (a) a^y}$$

$$\frac{dy}{dx} = \frac{1}{\ln (a) a^{\log_a (x)}}$$

$$\frac{dy}{dx} = \frac{1}{\ln (a) x}$$

 

[HallsofIvy]

but ln(5)= 1/ log₅(e) so if courtrigrad meant

$$\frac{1}{x log_5(e)}$$

that's completely correct.

 

[Sick0Fant]

I think this is it.

log(base 5)x=ln(x)/ln(5)
d/dx(ln(x)/ln(5)=1/(ln(5)x)

If not, then I'll hit myself over the head with my Calc book.

EDIT: I guess somebody pretty much said the same thing before I did... sorry.