# How would you graph f(x)= 2 ln x?

Jan 21, 2016

See the explanantion

#### Explanation:

To find the x-intercept mathematically

If $y = 2 \ln \left(x\right)$ then $\ln \left(x\right) = \frac{y}{2}$

Another way of writing this is:

${e}^{\frac{y}{2}} = x$.......................................(1)

The x-intercept is when $y = 0$ so equation (1) becomes:

${e}^{\frac{0}{2}} = {e}^{0} = 1 = x$

So the x-intercept is at $x = 1$
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You asked 'how' would you graph ....

The method would be to build a table of values.
The top row would have the values of x
The next row down would have the values of ln(x)
and the row below that would have the values of $2 \times \ln \left(x\right)$

This last row gives the values for $y$

You would then mark a series of points that maches both your value of $x$ and the calculated value of $y$

Your graph should look something like this: