Ln(7x-12)=lnx

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Solution for Ln(7x-12)=lnx equation: 


Simplifying
Ln(7x + -12) = lnx

Reorder the terms:
nL(-12 + 7x) = lnx
(-12 * nL + 7x * nL) = lnx
(-12nL + 7nxL) = lnx

Solving
-12nL + 7nxL = lnx

Solving for variable 'n'.

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

Add '-1lnx' to each side of the equation.
-12nL + -1lnx + 7nxL = lnx + -1lnx

Reorder the terms:
-1lnx + -12nL + 7nxL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1lnx + -12nL + 7nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1lx + -12L + 7xL) = 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 '(-1lx + -12L + 7xL)' equal to zero and attempt to solve:

Simplifying
-1lx + -12L + 7xL = 0

Reorder the terms:
-12L + -1lx + 7xL = 0

Solving
-12L + -1lx + 7xL = 0

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

Add '12L' to each side of the equation.
-12L + -1lx + 12L + 7xL = 0 + 12L

Reorder the terms:
-12L + 12L + -1lx + 7xL = 0 + 12L

Combine like terms: -12L + 12L = 0
0 + -1lx + 7xL = 0 + 12L
-1lx + 7xL = 0 + 12L
Remove the zero:
-1lx + 7xL = 12L

Add 'lx' to each side of the equation.
-1lx + lx + 7xL = 12L + lx

Combine like terms: -1lx + lx = 0
0 + 7xL = 12L + lx
7xL = 12L + lx

Add '-7xL' to each side of the equation.
7xL + -7xL = 12L + lx + -7xL

Combine like terms: 7xL + -7xL = 0
0 = 12L + lx + -7xL

Simplifying
0 = 12L + lx + -7xL

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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