Ln(6x+8)=ln(2x+15)

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Solution for Ln(6x+8)=ln(2x+15) equation: 


Simplifying
Ln(6x + 8) = ln(2x + 15)

Reorder the terms:
nL(8 + 6x) = ln(2x + 15)
(8 * nL + 6x * nL) = ln(2x + 15)
(8nL + 6nxL) = ln(2x + 15)

Reorder the terms:
8nL + 6nxL = ln(15 + 2x)
8nL + 6nxL = (15 * ln + 2x * ln)
8nL + 6nxL = (15ln + 2lnx)

Solving
8nL + 6nxL = 15ln + 2lnx

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.
8nL + -15ln + 6nxL = 15ln + -15ln + 2lnx

Reorder the terms:
-15ln + 8nL + 6nxL = 15ln + -15ln + 2lnx

Combine like terms: 15ln + -15ln = 0
-15ln + 8nL + 6nxL = 0 + 2lnx
-15ln + 8nL + 6nxL = 2lnx

Add '-2lnx' to each side of the equation.
-15ln + 8nL + -2lnx + 6nxL = 2lnx + -2lnx

Reorder the terms:
-15ln + -2lnx + 8nL + 6nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-15ln + -2lnx + 8nL + 6nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-15l + -2lx + 8L + 6xL) = 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 + -2lx + 8L + 6xL)' equal to zero and attempt to solve:

Simplifying
-15l + -2lx + 8L + 6xL = 0

Reorder the terms:
8L + -15l + -2lx + 6xL = 0

Solving
8L + -15l + -2lx + 6xL = 0

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

Add '-8L' to each side of the equation.
8L + -15l + -2lx + -8L + 6xL = 0 + -8L

Reorder the terms:
8L + -8L + -15l + -2lx + 6xL = 0 + -8L

Combine like terms: 8L + -8L = 0
0 + -15l + -2lx + 6xL = 0 + -8L
-15l + -2lx + 6xL = 0 + -8L
Remove the zero:
-15l + -2lx + 6xL = -8L

Add '15l' to each side of the equation.
-15l + -2lx + 15l + 6xL = -8L + 15l

Reorder the terms:
-15l + 15l + -2lx + 6xL = -8L + 15l

Combine like terms: -15l + 15l = 0
0 + -2lx + 6xL = -8L + 15l
-2lx + 6xL = -8L + 15l

Add '2lx' to each side of the equation.
-2lx + 2lx + 6xL = -8L + 15l + 2lx

Combine like terms: -2lx + 2lx = 0
0 + 6xL = -8L + 15l + 2lx
6xL = -8L + 15l + 2lx

Add '-6xL' to each side of the equation.
6xL + -6xL = -8L + 15l + 2lx + -6xL

Combine like terms: 6xL + -6xL = 0
0 = -8L + 15l + 2lx + -6xL

Simplifying
0 = -8L + 15l + 2lx + -6xL

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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