Ln(3x-7)=ln(5-x)

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Solution for Ln(3x-7)=ln(5-x) equation:


Simplifying
Ln(3x + -7) = ln(5 + -1x)

Reorder the terms:
nL(-7 + 3x) = ln(5 + -1x)
(-7 * nL + 3x * nL) = ln(5 + -1x)
(-7nL + 3nxL) = ln(5 + -1x)
-7nL + 3nxL = (5 * ln + -1x * ln)
-7nL + 3nxL = (5ln + -1lnx)

Solving
-7nL + 3nxL = 5ln + -1lnx

Solving for variable 'n'.

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

Add '-5ln' to each side of the equation.
-7nL + -5ln + 3nxL = 5ln + -5ln + -1lnx

Reorder the terms:
-5ln + -7nL + 3nxL = 5ln + -5ln + -1lnx

Combine like terms: 5ln + -5ln = 0
-5ln + -7nL + 3nxL = 0 + -1lnx
-5ln + -7nL + 3nxL = -1lnx

Add 'lnx' to each side of the equation.
-5ln + -7nL + lnx + 3nxL = -1lnx + lnx

Reorder the terms:
-5ln + lnx + -7nL + 3nxL = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-5ln + lnx + -7nL + 3nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5l + lx + -7L + 3xL) = 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 '(-5l + lx + -7L + 3xL)' equal to zero and attempt to solve: Simplifying -5l + lx + -7L + 3xL = 0 Reorder the terms: -7L + -5l + lx + 3xL = 0 Solving -7L + -5l + lx + 3xL = 0 Move all terms containing n to the left, all other terms to the right. Add '7L' to each side of the equation. -7L + -5l + lx + 7L + 3xL = 0 + 7L Reorder the terms: -7L + 7L + -5l + lx + 3xL = 0 + 7L Combine like terms: -7L + 7L = 0 0 + -5l + lx + 3xL = 0 + 7L -5l + lx + 3xL = 0 + 7L Remove the zero: -5l + lx + 3xL = 7L Add '5l' to each side of the equation. -5l + lx + 5l + 3xL = 7L + 5l Reorder the terms: -5l + 5l + lx + 3xL = 7L + 5l Combine like terms: -5l + 5l = 0 0 + lx + 3xL = 7L + 5l lx + 3xL = 7L + 5l Add '-1lx' to each side of the equation. lx + -1lx + 3xL = 7L + 5l + -1lx Combine like terms: lx + -1lx = 0 0 + 3xL = 7L + 5l + -1lx 3xL = 7L + 5l + -1lx Add '-3xL' to each side of the equation. 3xL + -3xL = 7L + 5l + -1lx + -3xL Combine like terms: 3xL + -3xL = 0 0 = 7L + 5l + -1lx + -3xL Simplifying 0 = 7L + 5l + -1lx + -3xL 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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