2
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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}]
  }
 ]
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  • $\begingroup$ 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. $\endgroup$ – David G. Stork May 14 at 1:55
3
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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}]}]

enter image description here

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