# Having trouble plotting a logarithmic equation

I want to plot these two logarithmic equations:

1. $$\log_{10}x^2 = 6$$

$$10^{\log_{10}x^2} = 10^6$$

$$x^2 = 10^6$$

$$x=\pm 10^3$$

This is my code for trying to plot this:

Plot[
{Log[x^2], 6},
{x, -5, 5},
Epilog ->
{
Red, PointSize @ 0.015, Point[{1000, -1000, 80}]
}
]

1. $$\log_{10}(z-3) = 2$$

Doing the same thing I get, $$z-3=100$$, so $$z-103$$

Similarly, my code for this is:

Plot[
{Log[z - 3], 2},
{z, -100, 100},
Epilog ->
{
Red, PointSize @ 0.015, Point[{103, 80}]
}
]

• It is meaningless to state you'll plot an "equation." Instead you plot a function. That is the source of your confusion, and why your code makes no sense. – David G. Stork May 14 '19 at 1:55

First, you don't need to do the algebra by hand:

Solve[Log10[x^2] == 6, x]
{{x -> -1000}, {x -> 1000}}


Then you can plot both sides of the equation, which I think is what you are looking for:

Plot[{Log[10, x^2], 6}, {x, -1200, 1200},
Epilog -> {Red, PointSize@0.015, Point[{1000, 6}], Point[{-1000, 6}]}] 