Ln(3x+1)=ln(x+7)

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Solution for Ln(3x+1)=ln(x+7) equation: 


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

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

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

Solving
1nL + 3nxL = 7ln + lnx

Solving for variable 'n'.

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-7l + -1lx + L + 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 '(-7l + -1lx + L + 3xL)' equal to zero and attempt to solve:

Simplifying
-7l + -1lx + L + 3xL = 0

Reorder the terms:
L + -7l + -1lx + 3xL = 0

Solving
L + -7l + -1lx + 3xL = 0

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

Add '-1L' to each side of the equation.
L + -7l + -1lx + -1L + 3xL = 0 + -1L

Reorder the terms:
L + -1L + -7l + -1lx + 3xL = 0 + -1L

Combine like terms: L + -1L = 0
0 + -7l + -1lx + 3xL = 0 + -1L
-7l + -1lx + 3xL = 0 + -1L
Remove the zero:
-7l + -1lx + 3xL = -1L

Add '7l' to each side of the equation.
-7l + -1lx + 7l + 3xL = -1L + 7l

Reorder the terms:
-7l + 7l + -1lx + 3xL = -1L + 7l

Combine like terms: -7l + 7l = 0
0 + -1lx + 3xL = -1L + 7l
-1lx + 3xL = -1L + 7l

Add 'lx' to each side of the equation.
-1lx + lx + 3xL = -1L + 7l + lx

Combine like terms: -1lx + lx = 0
0 + 3xL = -1L + 7l + lx
3xL = -1L + 7l + lx

Add '-3xL' to each side of the equation.
3xL + -3xL = -1L + 7l + lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = -1L + 7l + lx + -3xL

Simplifying
0 = -1L + 7l + lx + -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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