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what is the equation? \(2^y = 3~~or 2^y =x??\)
That is \(log_2 3 =y\) and its graph is a line.
Can't be one of the options.

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Other answers:

If the question is \(2^y =x \\y = log_2 x\) then, we can consider it is a function of x. But your equation is y = a number, not a function. Therefore, if it has a graph, the graph must be a horizontal straight line, not a curve as shown.
Or!! my knowledge is not enough to solve. I am sorry. Let's wait for @ganeshie8
The given graph must be a graph of \(f(x) = \log_2 x\) so that you can check its value at \(x=3\) and thus find \(y\), as Loser66 said. What properties of the \(\log_2 x\) can you think about that can help us eliminate the wrong choices? I'll start: it is not defined at \(x=0\), so it never crosses the line \(x=0\) (which is what you may know as the y-axis).
Why can't it be B or C?
They never really cross the line \(x=0\)... they're only moving along it. The curve will get reaaaaaaaally close to \(x=0\) but never will it touch it.
Why not A or B or D?
I'm not convinced.
Did she mention why it's C?
Why?
Do you know who to evaluate \(f(x) = \log_2 x \) at different points? Basically do you know how the log function works?
how*
Have you been taught about graphing functions?
And do you know about the logarithmic function?
Well, if for instance, I ask you what \(\log(1)\) is... what is it?
What?
How?
Why did you choose C?
Well, why did you choose A?
You shouldn't do that. For instance, the graph given in A crosses the y-axis.
C is correct simply because it is the graph of \(f(x) = \log_2 x \).
That's what I thought, but you didn't confirm!
  • phi
you want to chooses the graph that plots log base 2(x) you should look for the graph that goes through y=0 when x=1 and y=1 when x=2
  • phi
and y=2 when x= 4
You know that \(2^y = 3\) so \(y = \log_2 3\). Now you can graph \(f(x) = \log_2 x\) and find the value of \(f(x)\) at \(x = 3\).

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