ln(6x+36)=ln(4x+22)

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Solution for ln(6x+36)=ln(4x+22) equation: 


Simplifying
ln(6x + 36) = ln(4x + 22)

Reorder the terms:
ln(36 + 6x) = ln(4x + 22)
(36 * ln + 6x * ln) = ln(4x + 22)
(36ln + 6lnx) = ln(4x + 22)

Reorder the terms:
36ln + 6lnx = ln(22 + 4x)
36ln + 6lnx = (22 * ln + 4x * ln)
36ln + 6lnx = (22ln + 4lnx)

Solving
36ln + 6lnx = 22ln + 4lnx

Solving for variable 'l'.

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

Add '-22ln' to each side of the equation.
36ln + -22ln + 6lnx = 22ln + -22ln + 4lnx

Combine like terms: 36ln + -22ln = 14ln
14ln + 6lnx = 22ln + -22ln + 4lnx

Combine like terms: 22ln + -22ln = 0
14ln + 6lnx = 0 + 4lnx
14ln + 6lnx = 4lnx

Add '-4lnx' to each side of the equation.
14ln + 6lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 6lnx + -4lnx = 2lnx
14ln + 2lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
14ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(7 + x) = 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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Add '-1x' to each side of the equation.
x + -1x = -7 + -1x

Combine like terms: x + -1x = 0
0 = -7 + -1x

Simplifying
0 = -7 + -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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