Graphing Logs?

Question

Can someone please show me How to find points for this equation

f(x)=3+log2 X

Answer 1

Two options. Use only powers of 2 for X.

log2 8 = 3 because 2^3 = 8.

x f(x)
1/2 3+-1 = 2
1 3+0 = 3
2 3+1 = 4
4 3+2 = 5
8 3+3 = 6, etc.

Rewrite it in exponential form. Replace f(x) with y.

y = 3 + log2 x
y - 3 = log2 x
2^(y-3) = x

Pick values for y and figure out x. Be sure to plot the points as (x,y) though.

Answer 2

Well, I would guess that the part you find difficult is finding
"log base 2."

To calculate the log with base 2 of the number 16 (for example) using a calculator:

log2(16) = log(16) / log(2)

So, if you can calculate logs in base 10 or base e, then use those on the right side of this equation and you can find the log base 2 of 16 (or whatever number you want to use).

And, of course, to greate the graph, you will need to use a wide range of positive values for x. I say positive values because the log function is not defined for negative values.