ln(x^2)=ln(3x)

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Solution for ln(x^2)=ln(3x) equation: 


Simplifying
ln(x2) = ln(3x)

Multiply ln * x2
lnx2 = ln(3x)

Remove parenthesis around (3x)
lnx2 = ln * 3x

Reorder the terms for easier multiplication:
lnx2 = 3ln * x

Multiply ln * x
lnx2 = 3lnx

Solving
lnx2 = 3lnx

Solving for variable 'l'.

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

Add '-3lnx' to each side of the equation.
-3lnx + lnx2 = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-3lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'lnx'.
lnx(-3 + x) = 0


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

Simplifying
lnx = 0

Solving
lnx = 0

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

Simplifying
lnx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Add '-1x' to each side of the equation.
x + -1x = 3 + -1x

Combine like terms: x + -1x = 0
0 = 3 + -1x

Simplifying
0 = 3 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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