Ln(x^2-20)=lnX

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Solution for Ln(x^2-20)=lnX equation: 


Simplifying
Ln(x2 + -20) = lnX

Reorder the terms:
nL(-20 + x2) = lnX
(-20 * nL + x2 * nL) = lnX
(-20nL + nx2L) = lnX

Solving
-20nL + nx2L = lnX

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1lnX' to each side of the equation.
-20nL + -1lnX + nx2L = lnX + -1lnX

Reorder the terms:
-1lnX + -20nL + nx2L = lnX + -1lnX

Combine like terms: lnX + -1lnX = 0
-1lnX + -20nL + nx2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1lX + -20L + x2L) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

Move all terms containing n to the left, all other terms to the right.

Simplifying
n = 0

Subproblem 2
Set the factor '(-1lX + -20L + x2L)' equal to zero and attempt to solve:

Simplifying
-1lX + -20L + x2L = 0

Reorder the terms:
-20L + -1lX + x2L = 0

Solving
-20L + -1lX + x2L = 0

Move all terms containing n to the left, all other terms to the right.

Add '20L' to each side of the equation.
-20L + -1lX + 20L + x2L = 0 + 20L

Reorder the terms:
-20L + 20L + -1lX + x2L = 0 + 20L

Combine like terms: -20L + 20L = 0
0 + -1lX + x2L = 0 + 20L
-1lX + x2L = 0 + 20L
Remove the zero:
-1lX + x2L = 20L

Add 'lX' to each side of the equation.
-1lX + lX + x2L = 20L + lX

Combine like terms: -1lX + lX = 0
0 + x2L = 20L + lX
x2L = 20L + lX

Add '-1x2L' to each side of the equation.
x2L + -1x2L = 20L + lX + -1x2L

Combine like terms: x2L + -1x2L = 0
0 = 20L + lX + -1x2L

Simplifying
0 = 20L + lX + -1x2L

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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