ln(5x+12)-ln(x)=ln(6)

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Solution for ln(5x+12)-ln(x)=ln(6) equation: 


Simplifying
ln(5x + 12) + -1ln(x) = ln(6)

Reorder the terms:
ln(12 + 5x) + -1ln(x) = ln(6)
(12 * ln + 5x * ln) + -1ln(x) = ln(6)
(12ln + 5lnx) + -1ln(x) = ln(6)

Multiply ln * x
12ln + 5lnx + -1lnx = ln(6)

Combine like terms: 5lnx + -1lnx = 4lnx
12ln + 4lnx = ln(6)

Reorder the terms for easier multiplication:
12ln + 4lnx = 6ln

Solving
12ln + 4lnx = 6ln

Solving for variable 'l'.

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

Add '-6ln' to each side of the equation.
12ln + -6ln + 4lnx = 6ln + -6ln

Combine like terms: 12ln + -6ln = 6ln
6ln + 4lnx = 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
6ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(3 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Add '-2x' to each side of the equation.
2x + -2x = -3 + -2x

Combine like terms: 2x + -2x = 0
0 = -3 + -2x

Simplifying
0 = -3 + -2x

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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