Question

How do you graph y=8log10(0.1x+0.5) and y=2-x? and thus find the solution

Please include an explanation on what steps were taken to make the graph look the way it does

Answer 1

See below for a graph.

The solution is (x, y) = (2.844, -0.844).

Explanation:

A graphing calculator was used. The solution is in the area of the coordinate plane that this calculator shows by default, so the only "steps" were to enter the equations into the calculator. We highlighted the point of intersection of the function graphs so as to show the solution. (A different graphing calculator might need different steps to make it show the solution.)

We recognize that log10( ) is the same as log( ), since base 10 is the default for the log function.

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Some calculators will show the point of intersection to the full precision the calculator can provide. One such shows the solution to be ...

(x, y) = (2.84379161955, -0.84379161955)