2ln(x)=ln(x+20)

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


Simplifying
2ln(x) = ln(x + 20)

Multiply ln * x
2lnx = ln(x + 20)

Reorder the terms:
2lnx = ln(20 + x)
2lnx = (20 * ln + x * ln)
2lnx = (20ln + lnx)

Solving
2lnx = 20ln + lnx

Solving for variable 'l'.

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

Add '-20ln' to each side of the equation.
-20ln + 2lnx = 20ln + -20ln + lnx

Combine like terms: 20ln + -20ln = 0
-20ln + 2lnx = 0 + lnx
-20ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-20ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-20ln + 1lnx = lnx + -1lnx

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-20 + x) = 0


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

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 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 '(-20 + x)' equal to zero and attempt to solve:

Simplifying
-20 + x = 0

Solving
-20 + x = 0

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

Add '20' to each side of the equation.
-20 + 20 + x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + x = 0 + 20
x = 0 + 20

Combine like terms: 0 + 20 = 20
x = 20

Add '-1x' to each side of the equation.
x + -1x = 20 + -1x

Combine like terms: x + -1x = 0
0 = 20 + -1x

Simplifying
0 = 20 + -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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