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

1 Answer

Dec 20, 2016

As expressed this question does not make any sense.

Explanation:

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

It could be solved for $x$ $x$ as
$XXX 2^{x} - 5 < 64$ $color(white)("XXX")2^x-5 < 64$

$XXX \to 2^{x} < 69$ $color(white)("XXX")rarr 2^x < 69$

$XXX \to {log}_{2} 2^{x} < {log}_{2} 69$ $color(white)("XXX")rarr log_2 2^x < log_2 69$

$XXX \to x < {log}_{2} 69$ $color(white)("XXX")rarr x < log_2 69$

then using a calculator evaluating ${log}_{2} 69 \approx 6.108524457$ $log_2 69 ~~6.108524457$

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

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

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