# How do you sketch the graph of y=log_2(x+2)?

Nov 29, 2016

The graph of $y$ is the standard graph of $\ln x$ transformed 2 units left and scaled by $\frac{1}{\ln} 2$

#### Explanation:

To change the base of the log to base e:

${\log}_{2} x = \ln \frac{x}{\ln} 2$

In this example $y = {\log}_{2} \left(x + 2\right)$

$\therefore y = \ln \frac{x + 2}{\ln} 2$

The graph of $y$ is the standard graph of $\ln x$ transformed 2 units left and scaled by $\frac{1}{\ln} 2$

$y$ is defined for $x > - 2$
$y$ has a single zero at $x = - 1$
$y = 1$ at $x = 0$

The graph of $y$ is shown below

graph{ln(x+2)/ln2 [-10, 10, -5, 5]}

Nov 29, 2016

x-intercept is -1; y-intercept is 1.
As $x \to - 2 , y \to - \infty$; as $x \to \infty , y \to \infty$. Graph for the inverse $x = {2}^{y} - 1$ is inserted.

#### Explanation:

Cuts axes at (-1, 0) and (0, 1). x = -2 is the asymptote.

For graphing, I have used the inverse $x = {2}^{y} - 1$.

graph{2^y-x-2=0 [-10, 10, -5, 5]}