Ln(-5*x+7)=ln*2+ln*x

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Solution for Ln(-5*x+7)=ln*2+ln*x equation: 


Simplifying
Ln(-5x + 7) = ln * 2 + ln * x

Reorder the terms:
nL(7 + -5x) = ln * 2 + ln * x
(7 * nL + -5x * nL) = ln * 2 + ln * x
(7nL + -5nxL) = ln * 2 + ln * x

Reorder the terms for easier multiplication:
7nL + -5nxL = 2ln + ln * x

Multiply ln * x
7nL + -5nxL = 2ln + lnx

Solving
7nL + -5nxL = 2ln + lnx

Solving for variable 'n'.

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

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

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

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

Add '-1lnx' to each side of the equation.
-2ln + 7nL + -1lnx + -5nxL = lnx + -1lnx

Reorder the terms:
-2ln + -1lnx + 7nL + -5nxL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-2ln + -1lnx + 7nL + -5nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-2l + -1lx + 7L + -5xL) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-2l + -1lx + 7L + -5xL)' equal to zero and attempt to solve:

Simplifying
-2l + -1lx + 7L + -5xL = 0

Reorder the terms:
7L + -2l + -1lx + -5xL = 0

Solving
7L + -2l + -1lx + -5xL = 0

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

Add '-7L' to each side of the equation.
7L + -2l + -1lx + -7L + -5xL = 0 + -7L

Reorder the terms:
7L + -7L + -2l + -1lx + -5xL = 0 + -7L

Combine like terms: 7L + -7L = 0
0 + -2l + -1lx + -5xL = 0 + -7L
-2l + -1lx + -5xL = 0 + -7L
Remove the zero:
-2l + -1lx + -5xL = -7L

Add '2l' to each side of the equation.
-2l + -1lx + 2l + -5xL = -7L + 2l

Reorder the terms:
-2l + 2l + -1lx + -5xL = -7L + 2l

Combine like terms: -2l + 2l = 0
0 + -1lx + -5xL = -7L + 2l
-1lx + -5xL = -7L + 2l

Add 'lx' to each side of the equation.
-1lx + lx + -5xL = -7L + 2l + lx

Combine like terms: -1lx + lx = 0
0 + -5xL = -7L + 2l + lx
-5xL = -7L + 2l + lx

Add '5xL' to each side of the equation.
-5xL + 5xL = -7L + 2l + lx + 5xL

Combine like terms: -5xL + 5xL = 0
0 = -7L + 2l + lx + 5xL

Simplifying
0 = -7L + 2l + lx + 5xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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