2Ln(x-5)=Ln(7x)

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


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

Reorder the terms:
2nL(-5 + x) = Ln(7x)
(-5 * 2nL + x * 2nL) = Ln(7x)
(-10nL + 2nxL) = Ln(7x)

Remove parenthesis around (7x)
-10nL + 2nxL = nL * 7x

Reorder the terms for easier multiplication:
-10nL + 2nxL = 7nL * x

Multiply nL * x
-10nL + 2nxL = 7nxL

Solving
-10nL + 2nxL = 7nxL

Solving for variable 'n'.

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

Add '-7nxL' to each side of the equation.
-10nL + 2nxL + -7nxL = 7nxL + -7nxL

Combine like terms: 2nxL + -7nxL = -5nxL
-10nL + -5nxL = 7nxL + -7nxL

Combine like terms: 7nxL + -7nxL = 0
-10nL + -5nxL = 0

Factor out the Greatest Common Factor (GCF), '-5nL'.
-5nL(2 + x) = 0

Ignore the factor -5.

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

Simplifying
nL = 0

Solving
nL = 0

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

Simplifying
nL = 0

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Add '-1x' to each side of the equation.
x + -1x = -2 + -1x

Combine like terms: x + -1x = 0
0 = -2 + -1x

Simplifying
0 = -2 + -1x

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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