Why f(x)=ln(x^x) is not the same as g(x)=x·ln(x)?
There's a property in logaritms that says:
k·log_b(a)=log_b(a^k)
so g(x)=x·ln(x) should be the same as f(x)=ln(x^x) , but if we substitute some point we can easly see that it's not true, for example when x=-2 fuction g(x) has no solutions but fuction f(x) does:
g(-2)=-2ln(-2)=Undefi n ed
f(-2)=ln((-2)^(-2))=ln(1/4)~=-1.386
Why is that?
There's a property in logaritms that says:
so
Why is that?
1 Answer
Nov 22, 2017
Explanation:
This is a very good question. So, the function
Having this in mind you cannot replace the value for
in any of the 2 functions. Having put for
For
example: