Okay Some of these I know How to do but it takes sooo long so if you have any shortcuts TELL ME!! 1.32=2(base) 2.243 base 3 3.900 base 30 4.121 base 11. THANX!
The easiest way is to write down a sequence of all the powers of your bases, which you can get by continually multiplying by the base... Then it's position tells you what the power is...
E.g. powers of 2 are 2, 4, 8, 16, 32, 64, etc... (which we get by continually multiplying by 2).
Since 32 is in the 5th position, $\displaystyle 32=2^5$.
Similarly, the powers of 3 are 3, 9, 27, 81, 243, 729, etc... (which we get by continually multiplying by 3).
Since 243 is in the 5th position, $\displaystyle 243 = 3^5$.
Can you do it for powers of 11?
I am just starting sixth grade and I lost track of how to do bases and exponents, so I am very thankful. I now understand and appreciate your help.
Katie Hanks