Ln(X+1)+Ln(x+5)-ln(11X-1)=0

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Solution for Ln(X+1)+Ln(x+5)-ln(11X-1)=0 equation:


Simplifying
Ln(X + 1) + Ln(x + 5) + -1ln(11X + -1) = 0

Reorder the terms:
nL(1 + X) + Ln(x + 5) + -1ln(11X + -1) = 0
(1 * nL + X * nL) + Ln(x + 5) + -1ln(11X + -1) = 0
(1nL + nLX) + Ln(x + 5) + -1ln(11X + -1) = 0

Reorder the terms:
1nL + nLX + nL(5 + x) + -1ln(11X + -1) = 0
1nL + nLX + (5 * nL + x * nL) + -1ln(11X + -1) = 0
1nL + nLX + (5nL + nxL) + -1ln(11X + -1) = 0

Reorder the terms:
1nL + nLX + 5nL + nxL + -1ln(-1 + 11X) = 0
1nL + nLX + 5nL + nxL + (-1 * -1ln + 11X * -1ln) = 0
1nL + nLX + 5nL + nxL + (1ln + -11lnX) = 0

Reorder the terms:
1ln + -11lnX + 1nL + 5nL + nLX + nxL = 0

Combine like terms: 1nL + 5nL = 6nL
1ln + -11lnX + 6nL + nLX + nxL = 0

Solving
1ln + -11lnX + 6nL + nLX + nxL = 0

Solving for variable 'l'.

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

Add '-6nL' to each side of the equation.
1ln + -11lnX + 6nL + nLX + -6nL + nxL = 0 + -6nL

Reorder the terms:
1ln + -11lnX + 6nL + -6nL + nLX + nxL = 0 + -6nL

Combine like terms: 6nL + -6nL = 0
1ln + -11lnX + 0 + nLX + nxL = 0 + -6nL
1ln + -11lnX + nLX + nxL = 0 + -6nL
Remove the zero:
1ln + -11lnX + nLX + nxL = -6nL

Add '-1nLX' to each side of the equation.
1ln + -11lnX + nLX + -1nLX + nxL = -6nL + -1nLX

Combine like terms: nLX + -1nLX = 0
1ln + -11lnX + 0 + nxL = -6nL + -1nLX
1ln + -11lnX + nxL = -6nL + -1nLX

Add '-1nxL' to each side of the equation.
1ln + -11lnX + nxL + -1nxL = -6nL + -1nLX + -1nxL

Combine like terms: nxL + -1nxL = 0
1ln + -11lnX + 0 = -6nL + -1nLX + -1nxL
1ln + -11lnX = -6nL + -1nLX + -1nxL

Reorder the terms:
1ln + -11lnX + 6nL + nLX + nxL = -6nL + 6nL + -1nLX + nLX + -1nxL + nxL

Combine like terms: -6nL + 6nL = 0
1ln + -11lnX + 6nL + nLX + nxL = 0 + -1nLX + nLX + -1nxL + nxL
1ln + -11lnX + 6nL + nLX + nxL = -1nLX + nLX + -1nxL + nxL

Combine like terms: -1nLX + nLX = 0
1ln + -11lnX + 6nL + nLX + nxL = 0 + -1nxL + nxL
1ln + -11lnX + 6nL + nLX + nxL = -1nxL + nxL

Combine like terms: -1nxL + nxL = 0
1ln + -11lnX + 6nL + nLX + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(l + -11lX + 6L + LX + xL) = 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 '(l + -11lX + 6L + LX + xL)' equal to zero and attempt to solve: Simplifying l + -11lX + 6L + LX + xL = 0 Reorder the terms: 6L + LX + l + -11lX + xL = 0 Solving 6L + LX + l + -11lX + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-6L' to each side of the equation. 6L + LX + l + -11lX + -6L + xL = 0 + -6L Reorder the terms: 6L + -6L + LX + l + -11lX + xL = 0 + -6L Combine like terms: 6L + -6L = 0 0 + LX + l + -11lX + xL = 0 + -6L LX + l + -11lX + xL = 0 + -6L Remove the zero: LX + l + -11lX + xL = -6L Add '-1LX' to each side of the equation. LX + l + -11lX + -1LX + xL = -6L + -1LX Reorder the terms: LX + -1LX + l + -11lX + xL = -6L + -1LX Combine like terms: LX + -1LX = 0 0 + l + -11lX + xL = -6L + -1LX l + -11lX + xL = -6L + -1LX Add '-1xL' to each side of the equation. l + -11lX + xL + -1xL = -6L + -1LX + -1xL Combine like terms: xL + -1xL = 0 l + -11lX + 0 = -6L + -1LX + -1xL l + -11lX = -6L + -1LX + -1xL 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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