ln(3x-1)+ln(2x)=ln(8)

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Solution for ln(3x-1)+ln(2x)=ln(8) equation: 


Simplifying
ln(3x + -1) + ln(2x) = ln(8)

Reorder the terms:
ln(-1 + 3x) + ln(2x) = ln(8)
(-1 * ln + 3x * ln) + ln(2x) = ln(8)
(-1ln + 3lnx) + ln(2x) = ln(8)

Remove parenthesis around (2x)
-1ln + 3lnx + ln * 2x = ln(8)

Reorder the terms for easier multiplication:
-1ln + 3lnx + 2ln * x = ln(8)

Multiply ln * x
-1ln + 3lnx + 2lnx = ln(8)

Combine like terms: 3lnx + 2lnx = 5lnx
-1ln + 5lnx = ln(8)

Reorder the terms for easier multiplication:
-1ln + 5lnx = 8ln

Solving
-1ln + 5lnx = 8ln

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
-1ln + -8ln + 5lnx = 8ln + -8ln

Combine like terms: -1ln + -8ln = -9ln
-9ln + 5lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-9ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-9 + 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 '(-9 + 5x)' equal to zero and attempt to solve:

Simplifying
-9 + 5x = 0

Solving
-9 + 5x = 0

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

Add '9' to each side of the equation.
-9 + 9 + 5x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 5x = 0 + 9
5x = 0 + 9

Combine like terms: 0 + 9 = 9
5x = 9

Add '-5x' to each side of the equation.
5x + -5x = 9 + -5x

Combine like terms: 5x + -5x = 0
0 = 9 + -5x

Simplifying
0 = 9 + -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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