ln*(x-3)+ln*4=ln*12

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Solution for ln*(x-3)+ln*4=ln*12 equation:


Simplifying
ln(x + -3) + ln * 4 = ln * 12

Reorder the terms:
ln(-3 + x) + ln * 4 = ln * 12
(-3 * ln + x * ln) + ln * 4 = ln * 12
(-3ln + lnx) + ln * 4 = ln * 12

Reorder the terms for easier multiplication:
-3ln + lnx + 4ln = ln * 12

Reorder the terms:
-3ln + 4ln + lnx = ln * 12

Combine like terms: -3ln + 4ln = 1ln
1ln + lnx = ln * 12

Reorder the terms for easier multiplication:
1ln + lnx = 12ln

Solving
1ln + lnx = 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.
1ln + -12ln + lnx = 12ln + -12ln

Combine like terms: 1ln + -12ln = -11ln
-11ln + lnx = 12ln + -12ln

Combine like terms: 12ln + -12ln = 0
-11ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-11 + x) = 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 '(-11 + x)' equal to zero and attempt to solve: Simplifying -11 + x = 0 Solving -11 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Add '-1x' to each side of the equation. x + -1x = 11 + -1x Combine like terms: x + -1x = 0 0 = 11 + -1x Simplifying 0 = 11 + -1x 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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