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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