Ln(x+9)=ln(2x-7)

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Solution for Ln(x+9)=ln(2x-7) equation: 


Simplifying
Ln(x + 9) = ln(2x + -7)

Reorder the terms:
nL(9 + x) = ln(2x + -7)
(9 * nL + x * nL) = ln(2x + -7)
(9nL + nxL) = ln(2x + -7)

Reorder the terms:
9nL + nxL = ln(-7 + 2x)
9nL + nxL = (-7 * ln + 2x * ln)
9nL + nxL = (-7ln + 2lnx)

Solving
9nL + nxL = -7ln + 2lnx

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.
9nL + 7ln + nxL = -7ln + 7ln + 2lnx

Reorder the terms:
7ln + 9nL + nxL = -7ln + 7ln + 2lnx

Combine like terms: -7ln + 7ln = 0
7ln + 9nL + nxL = 0 + 2lnx
7ln + 9nL + nxL = 2lnx

Add '-2lnx' to each side of the equation.
7ln + 9nL + -2lnx + nxL = 2lnx + -2lnx

Reorder the terms:
7ln + -2lnx + 9nL + nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
7ln + -2lnx + 9nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(7l + -2lx + 9L + xL) = 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 + -2lx + 9L + xL)' equal to zero and attempt to solve:

Simplifying
7l + -2lx + 9L + xL = 0

Reorder the terms:
9L + 7l + -2lx + xL = 0

Solving
9L + 7l + -2lx + xL = 0

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

Add '-9L' to each side of the equation.
9L + 7l + -2lx + -9L + xL = 0 + -9L

Reorder the terms:
9L + -9L + 7l + -2lx + xL = 0 + -9L

Combine like terms: 9L + -9L = 0
0 + 7l + -2lx + xL = 0 + -9L
7l + -2lx + xL = 0 + -9L
Remove the zero:
7l + -2lx + xL = -9L

Add '-7l' to each side of the equation.
7l + -2lx + -7l + xL = -9L + -7l

Reorder the terms:
7l + -7l + -2lx + xL = -9L + -7l

Combine like terms: 7l + -7l = 0
0 + -2lx + xL = -9L + -7l
-2lx + xL = -9L + -7l

Add '2lx' to each side of the equation.
-2lx + 2lx + xL = -9L + -7l + 2lx

Combine like terms: -2lx + 2lx = 0
0 + xL = -9L + -7l + 2lx
xL = -9L + -7l + 2lx

Add '-1xL' to each side of the equation.
xL + -1xL = -9L + -7l + 2lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -9L + -7l + 2lx + -1xL

Simplifying
0 = -9L + -7l + 2lx + -1xL

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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