2ln(x-3)=ln(10x)

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Solution for 2ln(x-3)=ln(10x) equation: 


Simplifying
2ln(x + -3) = ln(10x)

Reorder the terms:
2ln(-3 + x) = ln(10x)
(-3 * 2ln + x * 2ln) = ln(10x)
(-6ln + 2lnx) = ln(10x)

Remove parenthesis around (10x)
-6ln + 2lnx = ln * 10x

Reorder the terms for easier multiplication:
-6ln + 2lnx = 10ln * x

Multiply ln * x
-6ln + 2lnx = 10lnx

Solving
-6ln + 2lnx = 10lnx

Solving for variable 'l'.

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

Add '-10lnx' to each side of the equation.
-6ln + 2lnx + -10lnx = 10lnx + -10lnx

Combine like terms: 2lnx + -10lnx = -8lnx
-6ln + -8lnx = 10lnx + -10lnx

Combine like terms: 10lnx + -10lnx = 0
-6ln + -8lnx = 0

Factor out the Greatest Common Factor (GCF), '-2ln'.
-2ln(3 + 4x) = 0

Ignore the factor -2.

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 '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Add '-4x' to each side of the equation.
4x + -4x = -3 + -4x

Combine like terms: 4x + -4x = 0
0 = -3 + -4x

Simplifying
0 = -3 + -4x

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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