2ln(x-3)=ln(30-2x)

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Solution for 2ln(x-3)=ln(30-2x) equation: 


Simplifying
2ln(x + -3) = ln(30 + -2x)

Reorder the terms:
2ln(-3 + x) = ln(30 + -2x)
(-3 * 2ln + x * 2ln) = ln(30 + -2x)
(-6ln + 2lnx) = ln(30 + -2x)
-6ln + 2lnx = (30 * ln + -2x * ln)
-6ln + 2lnx = (30ln + -2lnx)

Solving
-6ln + 2lnx = 30ln + -2lnx

Solving for variable 'l'.

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

Add '-30ln' to each side of the equation.
-6ln + -30ln + 2lnx = 30ln + -30ln + -2lnx

Combine like terms: -6ln + -30ln = -36ln
-36ln + 2lnx = 30ln + -30ln + -2lnx

Combine like terms: 30ln + -30ln = 0
-36ln + 2lnx = 0 + -2lnx
-36ln + 2lnx = -2lnx

Add '2lnx' to each side of the equation.
-36ln + 2lnx + 2lnx = -2lnx + 2lnx

Combine like terms: 2lnx + 2lnx = 4lnx
-36ln + 4lnx = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
-36ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), '4ln'.
4ln(-9 + x) = 0

Ignore the factor 4.

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 '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Add '-1x' to each side of the equation.
x + -1x = 9 + -1x

Combine like terms: x + -1x = 0
0 = 9 + -1x

Simplifying
0 = 9 + -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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