Question

I have no idea where to start on either of these problems. Would someone explain the steps to me? My teacher hasn’t gone over this yet and I’m very confused.

Answer 1

Problem 9: -1/2

Problem 10: 1/5

Explanation:

Problem 10: Label the given ln e^(1/5) as y = ln e^(1/5).

Write the identity e = e. Raise the first e to the power y and the second e to the power 1/5 (note that ln e^(1/5) = 1/5). Thus, we have:

e^y = e^(1/5), so that y = 1/5 (answer).

Problem 9: Let y = (log to the base 4 of) ∛1 / ∛8, or

y = (log to the base 4 of) ∛1 / ∛8, or

y = (log to the base 4 of) 1 /2

Write out the obvious:

4 = 4

Raise the first 4 to the power y and raise the second 4 to the power (log to the base 4 of) 1 /2. This results in:

4^y = 1/2. Solve this for y.

Note that 4^(1/2) = 2, so that 4^(-1/2) = 1/2

Thus, y = -1/2