Confirmation of Method

  • #1
1,235
1
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!
 

Answers and Replies

  • #2
Zurtex
Science Advisor
Homework Helper
1,120
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Well I don't actually see a method here, try and work it out:

[tex]y= \log_a (x)[/tex]

[tex]a^y = x[/tex]

[tex]\ln (a) a^y \frac{dy}{dx} = 1[/tex]

[tex]\frac{dy}{dx} = \frac{1}{\ln (a) a^y}[/tex]

[tex]\frac{dy}{dx} = \frac{1}{\ln (a) a^{\log_a (x)}}[/tex]

[tex]\frac{dy}{dx} = \frac{1}{\ln (a) x}[/tex]
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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but ln(5)= 1/ log5(e) so if courtrigrad meant

[tex]\frac{1}{x log_5(e)}[/tex]

that's completely correct.
 
  • #4
13
0
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.
 

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