ln(3x+8)-ln*x=ln*4

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Solution for ln(3x+8)-ln*x=ln*4 equation: 


Simplifying
ln(3x + 8) + -1ln * x = ln * 4

Reorder the terms:
ln(8 + 3x) + -1ln * x = ln * 4
(8 * ln + 3x * ln) + -1ln * x = ln * 4
(8ln + 3lnx) + -1ln * x = ln * 4

Multiply ln * x
8ln + 3lnx + -1lnx = ln * 4

Combine like terms: 3lnx + -1lnx = 2lnx
8ln + 2lnx = ln * 4

Reorder the terms for easier multiplication:
8ln + 2lnx = 4ln

Solving
8ln + 2lnx = 4ln

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
8ln + -4ln + 2lnx = 4ln + -4ln

Combine like terms: 8ln + -4ln = 4ln
4ln + 2lnx = 4ln + -4ln

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Add '-1x' to each side of the equation.
x + -1x = -2 + -1x

Combine like terms: x + -1x = 0
0 = -2 + -1x

Simplifying
0 = -2 + -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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