4.4: Graphs Of Logarithmic Functions - Mathematics LibreTexts

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Graph \(y=\log _{2} (x)\).

Solution:

To graph the function, we will first rewrite the logarithmic equation, \(y=\log _{2} (x)\), in exponential form, \(2^{y}=x\).

We will use point plotting to graph the function. It will be easier to start with values of \(y\) and then get \(x\).

\(y\) \(2^{y}=x\) \((x,y)\)
\(-2\) \(2^{-2}=\frac{1}{2^{2}}=\frac{1}{4}\) \((\frac{1}{4},2)\)
\(-1\) \(2^{-1}=\frac{1}{2^{1}}=\frac{1}{2}\) \((\frac{1}{2},-1)\)
\(0\) \(2^{0}=1\) \((1,0)\)
\(1\) \(2^{1}=2\) \((2,1)\)
\(2\) \(2^{2}=4\) \((4,2)\)
\(3\) \(2^{3}=8\) \((8,3)\)

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