Ln(x+19)=lnx(7x-8)

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Solution for Ln(x+19)=lnx(7x-8) equation: 


Simplifying
Ln(x + 19) = lnx(7x + -8)

Reorder the terms:
nL(19 + x) = lnx(7x + -8)
(19 * nL + x * nL) = lnx(7x + -8)
(19nL + nxL) = lnx(7x + -8)

Reorder the terms:
19nL + nxL = lnx(-8 + 7x)
19nL + nxL = (-8 * lnx + 7x * lnx)
19nL + nxL = (-8lnx + 7lnx2)

Solving
19nL + nxL = -8lnx + 7lnx2

Solving for variable 'n'.

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

Add '8lnx' to each side of the equation.
19nL + 8lnx + nxL = -8lnx + 8lnx + 7lnx2

Reorder the terms:
8lnx + 19nL + nxL = -8lnx + 8lnx + 7lnx2

Combine like terms: -8lnx + 8lnx = 0
8lnx + 19nL + nxL = 0 + 7lnx2
8lnx + 19nL + nxL = 7lnx2

Add '-7lnx2' to each side of the equation.
8lnx + 19nL + -7lnx2 + nxL = 7lnx2 + -7lnx2

Reorder the terms:
8lnx + -7lnx2 + 19nL + nxL = 7lnx2 + -7lnx2

Combine like terms: 7lnx2 + -7lnx2 = 0
8lnx + -7lnx2 + 19nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(8lx + -7lx2 + 19L + 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 '(8lx + -7lx2 + 19L + xL)' equal to zero and attempt to solve:

Simplifying
8lx + -7lx2 + 19L + xL = 0

Reorder the terms:
19L + 8lx + -7lx2 + xL = 0

Solving
19L + 8lx + -7lx2 + xL = 0

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

Add '-19L' to each side of the equation.
19L + 8lx + -7lx2 + -19L + xL = 0 + -19L

Reorder the terms:
19L + -19L + 8lx + -7lx2 + xL = 0 + -19L

Combine like terms: 19L + -19L = 0
0 + 8lx + -7lx2 + xL = 0 + -19L
8lx + -7lx2 + xL = 0 + -19L
Remove the zero:
8lx + -7lx2 + xL = -19L

Add '-8lx' to each side of the equation.
8lx + -7lx2 + -8lx + xL = -19L + -8lx

Reorder the terms:
8lx + -8lx + -7lx2 + xL = -19L + -8lx

Combine like terms: 8lx + -8lx = 0
0 + -7lx2 + xL = -19L + -8lx
-7lx2 + xL = -19L + -8lx

Add '7lx2' to each side of the equation.
-7lx2 + 7lx2 + xL = -19L + -8lx + 7lx2

Combine like terms: -7lx2 + 7lx2 = 0
0 + xL = -19L + -8lx + 7lx2
xL = -19L + -8lx + 7lx2

Add '-1xL' to each side of the equation.
xL + -1xL = -19L + -8lx + 7lx2 + -1xL

Combine like terms: xL + -1xL = 0
0 = -19L + -8lx + 7lx2 + -1xL

Simplifying
0 = -19L + -8lx + 7lx2 + -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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