ln(x+3)=ln(6x-5)

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Solution for ln(x+3)=ln(6x-5) equation: 


Simplifying
ln(x + 3) = ln(6x + -5)

Reorder the terms:
ln(3 + x) = ln(6x + -5)
(3 * ln + x * ln) = ln(6x + -5)
(3ln + lnx) = ln(6x + -5)

Reorder the terms:
3ln + lnx = ln(-5 + 6x)
3ln + lnx = (-5 * ln + 6x * ln)
3ln + lnx = (-5ln + 6lnx)

Solving
3ln + lnx = -5ln + 6lnx

Solving for variable 'l'.

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

Add '5ln' to each side of the equation.
3ln + 5ln + lnx = -5ln + 5ln + 6lnx

Combine like terms: 3ln + 5ln = 8ln
8ln + lnx = -5ln + 5ln + 6lnx

Combine like terms: -5ln + 5ln = 0
8ln + lnx = 0 + 6lnx
8ln + lnx = 6lnx

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

Combine like terms: lnx + -6lnx = -5lnx
8ln + -5lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
8ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(8 + -5x) = 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 '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Add '5x' to each side of the equation.
-5x + 5x = -8 + 5x

Combine like terms: -5x + 5x = 0
0 = -8 + 5x

Simplifying
0 = -8 + 5x

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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