ln(x-1)+ln(6)=ln(3x)

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Solution for ln(x-1)+ln(6)=ln(3x) equation: 


Simplifying
ln(x + -1) + ln(6) = ln(3x)

Reorder the terms:
ln(-1 + x) + ln(6) = ln(3x)
(-1 * ln + x * ln) + ln(6) = ln(3x)
(-1ln + lnx) + ln(6) = ln(3x)

Reorder the terms for easier multiplication:
-1ln + lnx + 6ln = ln(3x)

Reorder the terms:
-1ln + 6ln + lnx = ln(3x)

Combine like terms: -1ln + 6ln = 5ln
5ln + lnx = ln(3x)

Remove parenthesis around (3x)
5ln + lnx = ln * 3x

Reorder the terms for easier multiplication:
5ln + lnx = 3ln * x

Multiply ln * x
5ln + lnx = 3lnx

Solving
5ln + lnx = 3lnx

Solving for variable 'l'.

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

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

Combine like terms: lnx + -3lnx = -2lnx
5ln + -2lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
5ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -2x) = 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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Add '2x' to each side of the equation.
-2x + 2x = -5 + 2x

Combine like terms: -2x + 2x = 0
0 = -5 + 2x

Simplifying
0 = -5 + 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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