Ln(2x-1)+ln(x-5)-2lnx=0

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Solution for Ln(2x-1)+ln(x-5)-2lnx=0 equation: 


Simplifying
Ln(2x + -1) + ln(x + -5) + -2lnx = 0

Reorder the terms:
nL(-1 + 2x) + ln(x + -5) + -2lnx = 0
(-1 * nL + 2x * nL) + ln(x + -5) + -2lnx = 0
(-1nL + 2nxL) + ln(x + -5) + -2lnx = 0

Reorder the terms:
-1nL + 2nxL + ln(-5 + x) + -2lnx = 0
-1nL + 2nxL + (-5 * ln + x * ln) + -2lnx = 0
-1nL + 2nxL + (-5ln + lnx) + -2lnx = 0

Reorder the terms:
-5ln + lnx + -2lnx + -1nL + 2nxL = 0

Combine like terms: lnx + -2lnx = -1lnx
-5ln + -1lnx + -1nL + 2nxL = 0

Solving
-5ln + -1lnx + -1nL + 2nxL = 0

Solving for variable 'l'.

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

Add 'nL' to each side of the equation.
-5ln + -1lnx + -1nL + nL + 2nxL = 0 + nL

Combine like terms: -1nL + nL = 0
-5ln + -1lnx + 0 + 2nxL = 0 + nL
-5ln + -1lnx + 2nxL = 0 + nL
Remove the zero:
-5ln + -1lnx + 2nxL = nL

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

Combine like terms: 2nxL + -2nxL = 0
-5ln + -1lnx + 0 = nL + -2nxL
-5ln + -1lnx = nL + -2nxL

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

Combine like terms: nL + -1nL = 0
-5ln + -1lnx + -1nL + 2nxL = 0 + -2nxL + 2nxL
-5ln + -1lnx + -1nL + 2nxL = -2nxL + 2nxL

Combine like terms: -2nxL + 2nxL = 0
-5ln + -1lnx + -1nL + 2nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5l + -1lx + -1L + 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 '(-5l + -1lx + -1L + 2xL)' equal to zero and attempt to solve:

Simplifying
-5l + -1lx + -1L + 2xL = 0

Reorder the terms:
-1L + -5l + -1lx + 2xL = 0

Solving
-1L + -5l + -1lx + 2xL = 0

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

Add 'L' to each side of the equation.
-1L + -5l + -1lx + L + 2xL = 0 + L

Reorder the terms:
-1L + L + -5l + -1lx + 2xL = 0 + L

Combine like terms: -1L + L = 0
0 + -5l + -1lx + 2xL = 0 + L
-5l + -1lx + 2xL = 0 + L
Remove the zero:
-5l + -1lx + 2xL = L

Add '-2xL' to each side of the equation.
-5l + -1lx + 2xL + -2xL = L + -2xL

Combine like terms: 2xL + -2xL = 0
-5l + -1lx + 0 = L + -2xL
-5l + -1lx = L + -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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