Ln(4-x)=ln(x+8)+ln(2x+13)

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Solution for Ln(4-x)=ln(x+8)+ln(2x+13) equation:


Simplifying
Ln(4 + -1x) = ln(x + 8) + ln(2x + 13)
(4 * nL + -1x * nL) = ln(x + 8) + ln(2x + 13)
(4nL + -1nxL) = ln(x + 8) + ln(2x + 13)

Reorder the terms:
4nL + -1nxL = ln(8 + x) + ln(2x + 13)
4nL + -1nxL = (8 * ln + x * ln) + ln(2x + 13)
4nL + -1nxL = (8ln + lnx) + ln(2x + 13)

Reorder the terms:
4nL + -1nxL = 8ln + lnx + ln(13 + 2x)
4nL + -1nxL = 8ln + lnx + (13 * ln + 2x * ln)
4nL + -1nxL = 8ln + lnx + (13ln + 2lnx)

Reorder the terms:
4nL + -1nxL = 8ln + 13ln + lnx + 2lnx

Combine like terms: 8ln + 13ln = 21ln
4nL + -1nxL = 21ln + lnx + 2lnx

Combine like terms: lnx + 2lnx = 3lnx
4nL + -1nxL = 21ln + 3lnx

Solving
4nL + -1nxL = 21ln + 3lnx

Solving for variable 'n'.

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

Add '-21ln' to each side of the equation.
4nL + -21ln + -1nxL = 21ln + -21ln + 3lnx

Reorder the terms:
-21ln + 4nL + -1nxL = 21ln + -21ln + 3lnx

Combine like terms: 21ln + -21ln = 0
-21ln + 4nL + -1nxL = 0 + 3lnx
-21ln + 4nL + -1nxL = 3lnx

Add '-3lnx' to each side of the equation.
-21ln + 4nL + -3lnx + -1nxL = 3lnx + -3lnx

Reorder the terms:
-21ln + -3lnx + 4nL + -1nxL = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-21ln + -3lnx + 4nL + -1nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-21l + -3lx + 4L + -1xL) = 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 '(-21l + -3lx + 4L + -1xL)' equal to zero and attempt to solve: Simplifying -21l + -3lx + 4L + -1xL = 0 Reorder the terms: 4L + -21l + -3lx + -1xL = 0 Solving 4L + -21l + -3lx + -1xL = 0 Move all terms containing n to the left, all other terms to the right. Add '-4L' to each side of the equation. 4L + -21l + -3lx + -4L + -1xL = 0 + -4L Reorder the terms: 4L + -4L + -21l + -3lx + -1xL = 0 + -4L Combine like terms: 4L + -4L = 0 0 + -21l + -3lx + -1xL = 0 + -4L -21l + -3lx + -1xL = 0 + -4L Remove the zero: -21l + -3lx + -1xL = -4L Add '21l' to each side of the equation. -21l + -3lx + 21l + -1xL = -4L + 21l Reorder the terms: -21l + 21l + -3lx + -1xL = -4L + 21l Combine like terms: -21l + 21l = 0 0 + -3lx + -1xL = -4L + 21l -3lx + -1xL = -4L + 21l Add '3lx' to each side of the equation. -3lx + 3lx + -1xL = -4L + 21l + 3lx Combine like terms: -3lx + 3lx = 0 0 + -1xL = -4L + 21l + 3lx -1xL = -4L + 21l + 3lx Add 'xL' to each side of the equation. -1xL + xL = -4L + 21l + 3lx + xL Combine like terms: -1xL + xL = 0 0 = -4L + 21l + 3lx + xL Simplifying 0 = -4L + 21l + 3lx + xL 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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