Lnx^2=ln(x+20)

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Solution for Lnx^2=ln(x+20) equation: 


Simplifying
Lnx2 = ln(x + 20)

Reorder the terms:
nx2L = ln(20 + x)
nx2L = (20 * ln + x * ln)
nx2L = (20ln + lnx)

Solving
nx2L = 20ln + lnx

Solving for variable 'n'.

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

Add '-20ln' to each side of the equation.
-20ln + nx2L = 20ln + -20ln + lnx

Combine like terms: 20ln + -20ln = 0
-20ln + nx2L = 0 + lnx
-20ln + nx2L = lnx

Add '-1lnx' to each side of the equation.
-20ln + -1lnx + nx2L = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-20ln + -1lnx + nx2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-20l + -1lx + 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 '(-20l + -1lx + x2L)' equal to zero and attempt to solve:

Simplifying
-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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