# Confirmation of Method

1. Dec 7, 2004

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!

2. Dec 7, 2004

### Zurtex

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

$$y= \log_a (x)$$

$$a^y = x$$

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

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

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

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

3. Dec 8, 2004

### HallsofIvy

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

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

that's completely correct.

4. Dec 8, 2004

### 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.