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
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: