Question

True or False? If x>0, the (ln x) ^6 = 6lnx. Counter example?

Answer 1

False. It is only true if:
\[\ln(x^6)=6\ln(x)\]

Answer 2

agree

Answer 3

so its only when the variable is raised to a higher power and not if the whole ln is raised to a power?

Answer 4

counterexample:

what if x=e

Answer 5

\[(\ln(e))^6=1^6 \neq 6=6\ln(e)\]