Question

I know I need to use the change of base

Answer 1

The change of base formula looks like this:
                                           log x
(log to the base b of ) x = -----------    (you could also use ln instead of log)
                                            log b

                                                       log 40       1.602
Then (log to the base 7 of) 40 = ------------ = ------------- = 1.896   (answer)
                                                        log 7         0.8451

check (on calculator):    7^1.896 = 40.023   (close enough to 40 to verify 
                                                                     that this method "worked")