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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