I would be grateful if someone could tell me how to find unknown indices. e.g 3^x=9 (i know it is 2 but i would like to know the process for use with larger numbers). Thankyou in advance
No, you used the fact x=2. 9 = 3^x log 9 = log (3^x) log 9 = x log 3 x = log9/log3 = 2 log can be to any base as long as they are the same. you will usually find base 10, or base e on your calculator. log base e is usually ln.
1) 3^{x}=9 As long as we can think of the relationship between 3 and 9, we can solve this problem without using logarithm, like the one suggested by enslam. here are more examples (solve for x) 2) 5^{x} = 625 3) 4*5^{x} = 100 4) 2^{x} = 8 If you use Logarithm, in the step log9/log3, you need to know the fact that 9 = 3^2 too, unless you use a caculator.
That's true as long as the "opposite" problem, finding the power, can be done easily- as long as the answer is an integer as in all of your examples. To solve, for example 3^{x}= 7, you will need to use logarithms.