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

Answer:

Problem 9:  -1/2

Problem 10:  1/5

Step-by-step 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