For what value of x will the function y=log{base2}(x) first reach 4.
For what value of x will the function y=ln(x) first y=4?
For what x values will it first reach y=2 and y=3?
I read the stuff before this question and to be honest I am not sure that I understand a bit of it. What does the Log{base} mean? It says in the hand out that y=2^x and the inverse is y=log{base2} x....but I thought in a previous hand out that you said y=2^x would be the opposite of 2 Log(x)?
The log{base 2} function is what you get when you reverse the columns of the 2^x function--that is, it is the inverse of the 2^x function.
For example if x = -3 then 2^x = 1/8. The row [ -3 1/8 ] would appear in the 2^x table. So the row [ 1/8 -3 ] would appear in the log{base 2}(x) table, telling you that log{base 2} (1/8) = -3.
More generally the log{base b} function is what you get when you reverse the columns of the 2^x function--that is, it is the inverse of the b^x function.
One of the properties of logarithms is that log{base b}(x) = log(x) / log(b).
If b = 2 then you have the log{base 2} (x) = log(x) / log(2).
The quantity 2 log(x) you mention in your last sentence is the same as log(x^2), by the rule log(a^b) = b log(a). You might be confusing x^2 with 2^x.