Graph Using a Table of Values f(x)=2 log base 3 of x

$f (x) = 2 \log_{3} (x)$

Step 1

Substitute $1$ for $x$ and find the result for $y$ .

$y = 2 \log_{3} (1)$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$y = 2 \log_{3} (1)$

Simplify $2 \log_{3} (1)$ .

Logarithm base $3$ of $1$ is $0$ .

$y = 2 \cdot 0$

Multiply $2$ by $0$ .

$y = 0$

Step 3

Substitute $2$ for $x$ and find the result for $y$ .

$y = 2 \log_{3} (2)$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$y = 2 \log_{3} (2)$

Simplify $2 \log_{3} (2)$ .

Simplify $2 \log_{3} (2)$ by moving $2$ inside the logarithm.

$y = \log_{3} (2^{2})$

Raise $2$ to the power of $2$ .

$y = \log_{3} (4)$

Step 5

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ 1 & 0 \\ 2 & \log_{3} (4) \end{array}$

Step 6