Ln(4x+23)=ln(3x+15)

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Solution for Ln(4x+23)=ln(3x+15) equation: 


Simplifying
Ln(4x + 23) = ln(3x + 15)

Reorder the terms:
nL(23 + 4x) = ln(3x + 15)
(23 * nL + 4x * nL) = ln(3x + 15)
(23nL + 4nxL) = ln(3x + 15)

Reorder the terms:
23nL + 4nxL = ln(15 + 3x)
23nL + 4nxL = (15 * ln + 3x * ln)
23nL + 4nxL = (15ln + 3lnx)

Solving
23nL + 4nxL = 15ln + 3lnx

Solving for variable 'n'.

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

Add '-15ln' to each side of the equation.
23nL + -15ln + 4nxL = 15ln + -15ln + 3lnx

Reorder the terms:
-15ln + 23nL + 4nxL = 15ln + -15ln + 3lnx

Combine like terms: 15ln + -15ln = 0
-15ln + 23nL + 4nxL = 0 + 3lnx
-15ln + 23nL + 4nxL = 3lnx

Add '-3lnx' to each side of the equation.
-15ln + 23nL + -3lnx + 4nxL = 3lnx + -3lnx

Reorder the terms:
-15ln + -3lnx + 23nL + 4nxL = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-15ln + -3lnx + 23nL + 4nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-15l + -3lx + 23L + 4xL) = 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 '(-15l + -3lx + 23L + 4xL)' equal to zero and attempt to solve:

Simplifying
-15l + -3lx + 23L + 4xL = 0

Reorder the terms:
23L + -15l + -3lx + 4xL = 0

Solving
23L + -15l + -3lx + 4xL = 0

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

Add '-23L' to each side of the equation.
23L + -15l + -3lx + -23L + 4xL = 0 + -23L

Reorder the terms:
23L + -23L + -15l + -3lx + 4xL = 0 + -23L

Combine like terms: 23L + -23L = 0
0 + -15l + -3lx + 4xL = 0 + -23L
-15l + -3lx + 4xL = 0 + -23L
Remove the zero:
-15l + -3lx + 4xL = -23L

Add '15l' to each side of the equation.
-15l + -3lx + 15l + 4xL = -23L + 15l

Reorder the terms:
-15l + 15l + -3lx + 4xL = -23L + 15l

Combine like terms: -15l + 15l = 0
0 + -3lx + 4xL = -23L + 15l
-3lx + 4xL = -23L + 15l

Add '3lx' to each side of the equation.
-3lx + 3lx + 4xL = -23L + 15l + 3lx

Combine like terms: -3lx + 3lx = 0
0 + 4xL = -23L + 15l + 3lx
4xL = -23L + 15l + 3lx

Add '-4xL' to each side of the equation.
4xL + -4xL = -23L + 15l + 3lx + -4xL

Combine like terms: 4xL + -4xL = 0
0 = -23L + 15l + 3lx + -4xL

Simplifying
0 = -23L + 15l + 3lx + -4xL

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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