Final answer:
The expanded form of ln(√8t) is 2ln(2) + (1/2)ln(t).
Step-by-step explanation:
The natural logarithm of a number (ln) is the power to which e (approximately 2.71828) must be raised to equal the number.
To expand ln(√8t), we can rewrite it as ln(8t1/2) and then separate the terms using the properties of logarithms. ln(8) + ln(t1/2) = 2ln(2) + (1/2)ln(t).
So, the expanded form of ln(√8t) is 2ln(2) + (1/2)ln(t).