Ln(x+4)=ln(7x)

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Solution for Ln(x+4)=ln(7x) equation:


Simplifying
Ln(x + 4) = ln(7x)

Reorder the terms:
nL(4 + x) = ln(7x)
(4 * nL + x * nL) = ln(7x)
(4nL + nxL) = ln(7x)

Remove parenthesis around (7x)
4nL + nxL = ln * 7x

Reorder the terms for easier multiplication:
4nL + nxL = 7ln * x

Multiply ln * x
4nL + nxL = 7lnx

Solving
4nL + nxL = 7lnx

Solving for variable 'n'.

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

Add '-7lnx' to each side of the equation.
4nL + -7lnx + nxL = 7lnx + -7lnx

Reorder the terms:
-7lnx + 4nL + nxL = 7lnx + -7lnx

Combine like terms: 7lnx + -7lnx = 0
-7lnx + 4nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-7lx + 4L + xL) = 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 '(-7lx + 4L + xL)' equal to zero and attempt to solve: Simplifying -7lx + 4L + xL = 0 Reorder the terms: 4L + -7lx + xL = 0 Solving 4L + -7lx + xL = 0 Move all terms containing n to the left, all other terms to the right. Add '-4L' to each side of the equation. 4L + -7lx + -4L + xL = 0 + -4L Reorder the terms: 4L + -4L + -7lx + xL = 0 + -4L Combine like terms: 4L + -4L = 0 0 + -7lx + xL = 0 + -4L -7lx + xL = 0 + -4L Remove the zero: -7lx + xL = -4L Add '7lx' to each side of the equation. -7lx + 7lx + xL = -4L + 7lx Combine like terms: -7lx + 7lx = 0 0 + xL = -4L + 7lx xL = -4L + 7lx Add '-1xL' to each side of the equation. xL + -1xL = -4L + 7lx + -1xL Combine like terms: xL + -1xL = 0 0 = -4L + 7lx + -1xL Simplifying 0 = -4L + 7lx + -1xL 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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