$f(x) = \ln(x+1)$
Is there a way to transform the Equation above to a simpler one, that will include only $f(x) = g(x)\ln(x)$ kind of function?
Asked
Active
Viewed 128 times
0
-
1There is no "Equation above" – GFauxPas Oct 29 '16 at 22:53
-
the function is $ln(x+1)$ – Tom Oct 29 '16 at 22:54
-
2but $\ln (x+1)$ is defined for $ x=0$, while $f(x)\ln (x)$ isn't – Luca Oct 29 '16 at 22:55
-
ln(x+1) isn't an equation, neither is it a function if not defined else. It's a term. You have not defined f(x) = ln(x+1) – Martin Erhardt Oct 29 '16 at 22:56
-
edited, I meant $f(x) = ln(x+1)$ – Tom Oct 29 '16 at 22:57
-
1If you type \ln(x) instead of ln(x) it looks better: $\ln(x)$ vs $ln(x)$. – Oct 29 '16 at 22:58
1 Answers
2
If: $$\ln (x+1) = f(x) \ln x$$
then:
$$f(x) = \frac{\ln(x+1)}{\ln x}$$
This cannot be simplified. You could write $f(x) = \log_x(x+1)$, but we generally use logarithms with constant bases (hopefully $e$, that's the simplest base) so it is not a good idea to do so.
GFauxPas
- 5,047
-
-
1There are no log rules that would apply. Anything that might "look" simpler would just be hiding details from you without actually being simpler, like sneaking the same variable into the base and the exponent. – GFauxPas Oct 29 '16 at 23:09