ln(3x+8)=ln(6x-2)

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Solution for ln(3x+8)=ln(6x-2) equation: 


Simplifying
ln(3x + 8) = ln(6x + -2)

Reorder the terms:
ln(8 + 3x) = ln(6x + -2)
(8 * ln + 3x * ln) = ln(6x + -2)
(8ln + 3lnx) = ln(6x + -2)

Reorder the terms:
8ln + 3lnx = ln(-2 + 6x)
8ln + 3lnx = (-2 * ln + 6x * ln)
8ln + 3lnx = (-2ln + 6lnx)

Solving
8ln + 3lnx = -2ln + 6lnx

Solving for variable 'l'.

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

Add '2ln' to each side of the equation.
8ln + 2ln + 3lnx = -2ln + 2ln + 6lnx

Combine like terms: 8ln + 2ln = 10ln
10ln + 3lnx = -2ln + 2ln + 6lnx

Combine like terms: -2ln + 2ln = 0
10ln + 3lnx = 0 + 6lnx
10ln + 3lnx = 6lnx

Add '-6lnx' to each side of the equation.
10ln + 3lnx + -6lnx = 6lnx + -6lnx

Combine like terms: 3lnx + -6lnx = -3lnx
10ln + -3lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
10ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(10 + -3x) = 0


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 '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Add '3x' to each side of the equation.
-3x + 3x = -10 + 3x

Combine like terms: -3x + 3x = 0
0 = -10 + 3x

Simplifying
0 = -10 + 3x

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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