Question

question 3 · 1 point
which of the following equations uses the inverse property of logarithms correctly?
select all correct answers.
select all that apply:
(ln(11))^e = 11
ln(e^11) = 11
e^{ln(11)} = 11
ln(11^e) = 11

Explanation:

Step1: Recall inverse property rules

The inverse properties for natural logs/exponentials are: $\ln(e^x)=x$ and $e^{\ln(x)}=x$.

Step2: Check each option

• $(\ln(11))^e=11$: Violates order (log inside exp, not vice versa).
• $\ln(e^{11})=11$: Matches $\ln(e^x)=x$ (x=11).
• $e^{\ln(11)}=11$: Matches $e^{\ln(x)}=x$ (x=11).
• $\ln(11^e)=11$: Uses power rule ($e\ln11$), not inverse property.

Answer:

$\ln(e^{11}) = 11$, $e^{\ln(11)} = 11$