Now I found that the answer is 2 via trial and error. However, I wanted to know whether or not there was a formal mathematical procedure which proves my answer. I haven't been taught this unit yet, for the unit I'm working on now (involving inverse functions) hasn't been assigned yet. I've just been working ahead.
Thanks for the replies. I was just wondering if there were certain steps to be shown in order to get the answer. One of the questions asks:
, determine m.
The answer is .
How would I determine the answer of this question, without using the back of the book?
Since I do a bit of computer programming, some powers of 2 are very easy to recognize... someone will probably post a more general method after me, but tricks like this can often be used (express the base, in this case 8, as a smaller base raised to a power, in this case ).
If the problem does not come out so evenly, like maybe 3^x=17, you can just take the log (to any base) of both sides and solve for x. So, if a and b are constants, and
the solution is:
Of course, that's more work than you need to do for a case like 9^x=81.