Ln(6x-1)=on(x+14)

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Solution for Ln(6x-1)=on(x+14) equation:


Simplifying
Ln(6x + -1) = on(x + 14)

Reorder the terms:
nL(-1 + 6x) = on(x + 14)
(-1 * nL + 6x * nL) = on(x + 14)
(-1nL + 6nxL) = on(x + 14)

Reorder the terms:
-1nL + 6nxL = no(14 + x)
-1nL + 6nxL = (14 * no + x * no)
-1nL + 6nxL = (14no + nox)

Solving
-1nL + 6nxL = 14no + nox

Solving for variable 'n'.

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

Add '-14no' to each side of the equation.
-1nL + -14no + 6nxL = 14no + -14no + nox

Combine like terms: 14no + -14no = 0
-1nL + -14no + 6nxL = 0 + nox
-1nL + -14no + 6nxL = nox

Add '-1nox' to each side of the equation.
-1nL + -14no + -1nox + 6nxL = nox + -1nox

Combine like terms: nox + -1nox = 0
-1nL + -14no + -1nox + 6nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1L + -14o + -1ox + 6xL) = 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 '(-1L + -14o + -1ox + 6xL)' equal to zero and attempt to solve: Simplifying -1L + -14o + -1ox + 6xL = 0 Solving -1L + -14o + -1ox + 6xL = 0 Move all terms containing n to the left, all other terms to the right. Add 'L' to each side of the equation. -1L + -14o + -1ox + L + 6xL = 0 + L Reorder the terms: -1L + L + -14o + -1ox + 6xL = 0 + L Combine like terms: -1L + L = 0 0 + -14o + -1ox + 6xL = 0 + L -14o + -1ox + 6xL = 0 + L Remove the zero: -14o + -1ox + 6xL = L Add '14o' to each side of the equation. -14o + -1ox + 14o + 6xL = L + 14o Reorder the terms: -14o + 14o + -1ox + 6xL = L + 14o Combine like terms: -14o + 14o = 0 0 + -1ox + 6xL = L + 14o -1ox + 6xL = L + 14o Add 'ox' to each side of the equation. -1ox + ox + 6xL = L + 14o + ox Combine like terms: -1ox + ox = 0 0 + 6xL = L + 14o + ox 6xL = L + 14o + ox Add '-6xL' to each side of the equation. 6xL + -6xL = L + 14o + ox + -6xL Combine like terms: 6xL + -6xL = 0 0 = L + 14o + ox + -6xL Simplifying 0 = L + 14o + ox + -6xL 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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