all logarithms are is a fancy way of writing a power. what happens is the that base of the log is 10, which would be 10 raised to a power. the number the follows the log is the answer, so when you do the log of 4 on your calculator, you are finding 10^what ever power=4.
to help with those two problems, what you need to do is remember the fact that logs are exponents. so if you have 2log4=x, it is also equalivent to log16=x. that can also be reversed, and log100 would be 2log10.
the first one, what you would do is take the log of both sides, so you get:
log(a^x)=log(10^[2x+1])
which with what I stated above can be simplified to:
x*log(a)=2x+1*log(10)
being that logarithms have a given base of 10 (except for natural logs- ln, and logs with subscript after them that specifies the base) you now have:
x*log(a)=)2x+1)*1
which with some basic math, you finally get
log(a)=x+.5
and again using the rule of logs from the second paragraph you get:
a=10^(x+.5)
now b is a little more complex looking, but it is the same concept. You have to remember that logs can be added, subtracted, and multiplied just like exponents.
2*log(2x)=1+log(a)
subtract 1 from each side
2*log(2x)-1=log(a)
now just use the fundamental rule of logs to get:
a=10^(2*log(2x)-1)
and there you go.
hope this helps.