Ln*(2x+5)-ln*(6x+1)=ln*6

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Solution for Ln*(2x+5)-ln*(6x+1)=ln*6 equation:


Simplifying
Ln(2x + 5) + -1ln(6x + 1) = ln * 6

Reorder the terms:
nL(5 + 2x) + -1ln(6x + 1) = ln * 6
(5 * nL + 2x * nL) + -1ln(6x + 1) = ln * 6
(5nL + 2nxL) + -1ln(6x + 1) = ln * 6

Reorder the terms:
5nL + 2nxL + -1ln(1 + 6x) = ln * 6
5nL + 2nxL + (1 * -1ln + 6x * -1ln) = ln * 6
5nL + 2nxL + (-1ln + -6lnx) = ln * 6

Reorder the terms:
-1ln + -6lnx + 5nL + 2nxL = ln * 6

Reorder the terms for easier multiplication:
-1ln + -6lnx + 5nL + 2nxL = 6ln

Solving
-1ln + -6lnx + 5nL + 2nxL = 6ln

Solving for variable 'l'.

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

Add '-6ln' to each side of the equation.
-1ln + -6lnx + 5nL + -6ln + 2nxL = 6ln + -6ln

Reorder the terms:
-1ln + -6ln + -6lnx + 5nL + 2nxL = 6ln + -6ln

Combine like terms: -1ln + -6ln = -7ln
-7ln + -6lnx + 5nL + 2nxL = 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
-7ln + -6lnx + 5nL + 2nxL = 0

Add '-5nL' to each side of the equation.
-7ln + -6lnx + 5nL + -5nL + 2nxL = 0 + -5nL

Combine like terms: 5nL + -5nL = 0
-7ln + -6lnx + 0 + 2nxL = 0 + -5nL
-7ln + -6lnx + 2nxL = 0 + -5nL
Remove the zero:
-7ln + -6lnx + 2nxL = -5nL

Add '-2nxL' to each side of the equation.
-7ln + -6lnx + 2nxL + -2nxL = -5nL + -2nxL

Combine like terms: 2nxL + -2nxL = 0
-7ln + -6lnx + 0 = -5nL + -2nxL
-7ln + -6lnx = -5nL + -2nxL

Reorder the terms:
-7ln + -6lnx + 5nL + 2nxL = -5nL + 5nL + -2nxL + 2nxL

Combine like terms: -5nL + 5nL = 0
-7ln + -6lnx + 5nL + 2nxL = 0 + -2nxL + 2nxL
-7ln + -6lnx + 5nL + 2nxL = -2nxL + 2nxL

Combine like terms: -2nxL + 2nxL = 0
-7ln + -6lnx + 5nL + 2nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-7l + -6lx + 5L + 2xL) = 0

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(-7l + -6lx + 5L + 2xL)' equal to zero and attempt to solve: Simplifying -7l + -6lx + 5L + 2xL = 0 Reorder the terms: 5L + -7l + -6lx + 2xL = 0 Solving 5L + -7l + -6lx + 2xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-5L' to each side of the equation. 5L + -7l + -6lx + -5L + 2xL = 0 + -5L Reorder the terms: 5L + -5L + -7l + -6lx + 2xL = 0 + -5L Combine like terms: 5L + -5L = 0 0 + -7l + -6lx + 2xL = 0 + -5L -7l + -6lx + 2xL = 0 + -5L Remove the zero: -7l + -6lx + 2xL = -5L Add '-2xL' to each side of the equation. -7l + -6lx + 2xL + -2xL = -5L + -2xL Combine like terms: 2xL + -2xL = 0 -7l + -6lx + 0 = -5L + -2xL -7l + -6lx = -5L + -2xL 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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