# How do you write an equation of a line going through 2^x-5<64?

Dec 20, 2016

As expressed this question does not make any sense.

#### Explanation:

${2}^{x} - 5 < 64$ is not a point.

It could be solved for $x$ as
$\textcolor{w h i t e}{\text{XXX}} {2}^{x} - 5 < 64$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow {2}^{x} < 69$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow {\log}_{2} {2}^{x} < {\log}_{2} 69$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow x < {\log}_{2} 69$

then using a calculator evaluating ${\log}_{2} 69 \approx 6.108524457$

In the Cartesian plane this is a region composed of all points to the left of $x = 6.108524457$ (approx.)

I suppose you could argue that the equation $x = 0$ (for example) is the equation of a line going through (i.e. completely contained in) this region.