Ln(3x+7)=ln(5x-10)

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Solution for Ln(3x+7)=ln(5x-10) equation: 


Simplifying
Ln(3x + 7) = ln(5x + -10)

Reorder the terms:
nL(7 + 3x) = ln(5x + -10)
(7 * nL + 3x * nL) = ln(5x + -10)
(7nL + 3nxL) = ln(5x + -10)

Reorder the terms:
7nL + 3nxL = ln(-10 + 5x)
7nL + 3nxL = (-10 * ln + 5x * ln)
7nL + 3nxL = (-10ln + 5lnx)

Solving
7nL + 3nxL = -10ln + 5lnx

Solving for variable 'n'.

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

Add '10ln' to each side of the equation.
7nL + 10ln + 3nxL = -10ln + 10ln + 5lnx

Reorder the terms:
10ln + 7nL + 3nxL = -10ln + 10ln + 5lnx

Combine like terms: -10ln + 10ln = 0
10ln + 7nL + 3nxL = 0 + 5lnx
10ln + 7nL + 3nxL = 5lnx

Add '-5lnx' to each side of the equation.
10ln + 7nL + -5lnx + 3nxL = 5lnx + -5lnx

Reorder the terms:
10ln + -5lnx + 7nL + 3nxL = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
10ln + -5lnx + 7nL + 3nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(10l + -5lx + 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 '(10l + -5lx + 7L + 3xL)' equal to zero and attempt to solve:

Simplifying
10l + -5lx + 7L + 3xL = 0

Reorder the terms:
7L + 10l + -5lx + 3xL = 0

Solving
7L + 10l + -5lx + 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 + 10l + -5lx + -7L + 3xL = 0 + -7L

Reorder the terms:
7L + -7L + 10l + -5lx + 3xL = 0 + -7L

Combine like terms: 7L + -7L = 0
0 + 10l + -5lx + 3xL = 0 + -7L
10l + -5lx + 3xL = 0 + -7L
Remove the zero:
10l + -5lx + 3xL = -7L

Add '-10l' to each side of the equation.
10l + -5lx + -10l + 3xL = -7L + -10l

Reorder the terms:
10l + -10l + -5lx + 3xL = -7L + -10l

Combine like terms: 10l + -10l = 0
0 + -5lx + 3xL = -7L + -10l
-5lx + 3xL = -7L + -10l

Add '5lx' to each side of the equation.
-5lx + 5lx + 3xL = -7L + -10l + 5lx

Combine like terms: -5lx + 5lx = 0
0 + 3xL = -7L + -10l + 5lx
3xL = -7L + -10l + 5lx

Add '-3xL' to each side of the equation.
3xL + -3xL = -7L + -10l + 5lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = -7L + -10l + 5lx + -3xL

Simplifying
0 = -7L + -10l + 5lx + -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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