ln(x-5)+ln(2x)=ln(12)

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Solution for ln(x-5)+ln(2x)=ln(12) equation:


Simplifying
ln(x + -5) + ln(2x) = ln(12)

Reorder the terms:
ln(-5 + x) + ln(2x) = ln(12)
(-5 * ln + x * ln) + ln(2x) = ln(12)
(-5ln + lnx) + ln(2x) = ln(12)

Remove parenthesis around (2x)
-5ln + lnx + ln * 2x = ln(12)

Reorder the terms for easier multiplication:
-5ln + lnx + 2ln * x = ln(12)

Multiply ln * x
-5ln + lnx + 2lnx = ln(12)

Combine like terms: lnx + 2lnx = 3lnx
-5ln + 3lnx = ln(12)

Reorder the terms for easier multiplication:
-5ln + 3lnx = 12ln

Solving
-5ln + 3lnx = 12ln

Solving for variable 'l'.

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

Add '-12ln' to each side of the equation.
-5ln + -12ln + 3lnx = 12ln + -12ln

Combine like terms: -5ln + -12ln = -17ln
-17ln + 3lnx = 12ln + -12ln

Combine like terms: 12ln + -12ln = 0
-17ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-17 + 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 '(-17 + 3x)' equal to zero and attempt to solve: Simplifying -17 + 3x = 0 Solving -17 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 3x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 3x = 0 + 17 3x = 0 + 17 Combine like terms: 0 + 17 = 17 3x = 17 Add '-3x' to each side of the equation. 3x + -3x = 17 + -3x Combine like terms: 3x + -3x = 0 0 = 17 + -3x Simplifying 0 = 17 + -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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