Ln(2x-3)+ln(x+4)=ln(2x^2+1)

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Solution for Ln(2x-3)+ln(x+4)=ln(2x^2+1) equation: 


Simplifying
Ln(2x + -3) + ln(x + 4) = ln(2x2 + 1)

Reorder the terms:
nL(-3 + 2x) + ln(x + 4) = ln(2x2 + 1)
(-3 * nL + 2x * nL) + ln(x + 4) = ln(2x2 + 1)
(-3nL + 2nxL) + ln(x + 4) = ln(2x2 + 1)

Reorder the terms:
-3nL + 2nxL + ln(4 + x) = ln(2x2 + 1)
-3nL + 2nxL + (4 * ln + x * ln) = ln(2x2 + 1)
-3nL + 2nxL + (4ln + lnx) = ln(2x2 + 1)

Reorder the terms:
4ln + lnx + -3nL + 2nxL = ln(2x2 + 1)

Reorder the terms:
4ln + lnx + -3nL + 2nxL = ln(1 + 2x2)
4ln + lnx + -3nL + 2nxL = (1 * ln + 2x2 * ln)
4ln + lnx + -3nL + 2nxL = (1ln + 2lnx2)

Solving
4ln + lnx + -3nL + 2nxL = 1ln + 2lnx2

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
4ln + lnx + -3nL + -1ln + 2nxL = 1ln + -1ln + 2lnx2

Reorder the terms:
4ln + -1ln + lnx + -3nL + 2nxL = 1ln + -1ln + 2lnx2

Combine like terms: 4ln + -1ln = 3ln
3ln + lnx + -3nL + 2nxL = 1ln + -1ln + 2lnx2

Combine like terms: 1ln + -1ln = 0
3ln + lnx + -3nL + 2nxL = 0 + 2lnx2
3ln + lnx + -3nL + 2nxL = 2lnx2

Add '-2lnx2' to each side of the equation.
3ln + lnx + -3nL + -2lnx2 + 2nxL = 2lnx2 + -2lnx2

Reorder the terms:
3ln + lnx + -2lnx2 + -3nL + 2nxL = 2lnx2 + -2lnx2

Combine like terms: 2lnx2 + -2lnx2 = 0
3ln + lnx + -2lnx2 + -3nL + 2nxL = 0

Add '3nL' to each side of the equation.
3ln + lnx + -2lnx2 + -3nL + 3nL + 2nxL = 0 + 3nL

Combine like terms: -3nL + 3nL = 0
3ln + lnx + -2lnx2 + 0 + 2nxL = 0 + 3nL
3ln + lnx + -2lnx2 + 2nxL = 0 + 3nL
Remove the zero:
3ln + lnx + -2lnx2 + 2nxL = 3nL

Add '-2nxL' to each side of the equation.
3ln + lnx + -2lnx2 + 2nxL + -2nxL = 3nL + -2nxL

Combine like terms: 2nxL + -2nxL = 0
3ln + lnx + -2lnx2 + 0 = 3nL + -2nxL
3ln + lnx + -2lnx2 = 3nL + -2nxL

Reorder the terms:
3ln + lnx + -2lnx2 + -3nL + 2nxL = 3nL + -3nL + -2nxL + 2nxL

Combine like terms: 3nL + -3nL = 0
3ln + lnx + -2lnx2 + -3nL + 2nxL = 0 + -2nxL + 2nxL
3ln + lnx + -2lnx2 + -3nL + 2nxL = -2nxL + 2nxL

Combine like terms: -2nxL + 2nxL = 0
3ln + lnx + -2lnx2 + -3nL + 2nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(3l + lx + -2lx2 + -3L + 2xL) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(3l + lx + -2lx2 + -3L + 2xL)' equal to zero and attempt to solve:

Simplifying
3l + lx + -2lx2 + -3L + 2xL = 0

Reorder the terms:
-3L + 3l + lx + -2lx2 + 2xL = 0

Solving
-3L + 3l + lx + -2lx2 + 2xL = 0

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

Add '3L' to each side of the equation.
-3L + 3l + lx + -2lx2 + 3L + 2xL = 0 + 3L

Reorder the terms:
-3L + 3L + 3l + lx + -2lx2 + 2xL = 0 + 3L

Combine like terms: -3L + 3L = 0
0 + 3l + lx + -2lx2 + 2xL = 0 + 3L
3l + lx + -2lx2 + 2xL = 0 + 3L
Remove the zero:
3l + lx + -2lx2 + 2xL = 3L

Add '-2xL' to each side of the equation.
3l + lx + -2lx2 + 2xL + -2xL = 3L + -2xL

Combine like terms: 2xL + -2xL = 0
3l + lx + -2lx2 + 0 = 3L + -2xL
3l + lx + -2lx2 = 3L + -2xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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