Ln(2x+1)+ln(x-7)-2lnx=0

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Solution for Ln(2x+1)+ln(x-7)-2lnx=0 equation:


Simplifying
Ln(2x + 1) + ln(x + -7) + -2lnx = 0

Reorder the terms:
nL(1 + 2x) + ln(x + -7) + -2lnx = 0
(1 * nL + 2x * nL) + ln(x + -7) + -2lnx = 0
(1nL + 2nxL) + ln(x + -7) + -2lnx = 0

Reorder the terms:
1nL + 2nxL + ln(-7 + x) + -2lnx = 0
1nL + 2nxL + (-7 * ln + x * ln) + -2lnx = 0
1nL + 2nxL + (-7ln + lnx) + -2lnx = 0

Reorder the terms:
-7ln + lnx + -2lnx + 1nL + 2nxL = 0

Combine like terms: lnx + -2lnx = -1lnx
-7ln + -1lnx + 1nL + 2nxL = 0

Solving
-7ln + -1lnx + 1nL + 2nxL = 0

Solving for variable 'l'.

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

Add '-1nL' to each side of the equation.
-7ln + -1lnx + 1nL + -1nL + 2nxL = 0 + -1nL

Combine like terms: 1nL + -1nL = 0
-7ln + -1lnx + 0 + 2nxL = 0 + -1nL
-7ln + -1lnx + 2nxL = 0 + -1nL
Remove the zero:
-7ln + -1lnx + 2nxL = -1nL

Add '-2nxL' to each side of the equation.
-7ln + -1lnx + 2nxL + -2nxL = -1nL + -2nxL

Combine like terms: 2nxL + -2nxL = 0
-7ln + -1lnx + 0 = -1nL + -2nxL
-7ln + -1lnx = -1nL + -2nxL

Reorder the terms:
-7ln + -1lnx + nL + 2nxL = -1nL + nL + -2nxL + 2nxL

Combine like terms: -1nL + nL = 0
-7ln + -1lnx + nL + 2nxL = 0 + -2nxL + 2nxL
-7ln + -1lnx + nL + 2nxL = -2nxL + 2nxL

Combine like terms: -2nxL + 2nxL = 0
-7ln + -1lnx + nL + 2nxL = 0

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