12lnx-lnx^10=ln(3x+18)

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Solution for 12lnx-lnx^10=ln(3x+18) equation: 


Simplifying
12lnx + -1lnx10 = ln(3x + 18)

Reorder the terms:
12lnx + -1lnx10 = ln(18 + 3x)
12lnx + -1lnx10 = (18 * ln + 3x * ln)
12lnx + -1lnx10 = (18ln + 3lnx)

Solving
12lnx + -1lnx10 = 18ln + 3lnx

Solving for variable 'l'.

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

Add '-18ln' to each side of the equation.
12lnx + -18ln + -1lnx10 = 18ln + -18ln + 3lnx

Reorder the terms:
-18ln + 12lnx + -1lnx10 = 18ln + -18ln + 3lnx

Combine like terms: 18ln + -18ln = 0
-18ln + 12lnx + -1lnx10 = 0 + 3lnx
-18ln + 12lnx + -1lnx10 = 3lnx

Add '-3lnx' to each side of the equation.
-18ln + 12lnx + -3lnx + -1lnx10 = 3lnx + -3lnx

Combine like terms: 12lnx + -3lnx = 9lnx
-18ln + 9lnx + -1lnx10 = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-18ln + 9lnx + -1lnx10 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-18 + 9x + -1x10) = 0


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

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

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 '(-18 + 9x + -1x10)' equal to zero and attempt to solve:

Simplifying
-18 + 9x + -1x10 = 0

Solving
-18 + 9x + -1x10 = 0

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

Add '18' to each side of the equation.
-18 + 9x + 18 + -1x10 = 0 + 18

Reorder the terms:
-18 + 18 + 9x + -1x10 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 9x + -1x10 = 0 + 18
9x + -1x10 = 0 + 18

Combine like terms: 0 + 18 = 18
9x + -1x10 = 18

Add '-9x' to each side of the equation.
9x + -9x + -1x10 = 18 + -9x

Combine like terms: 9x + -9x = 0
0 + -1x10 = 18 + -9x
-1x10 = 18 + -9x

Add 'x10' to each side of the equation.
-1x10 + x10 = 18 + -9x + x10

Combine like terms: -1x10 + x10 = 0
0 = 18 + -9x + x10

Simplifying
0 = 18 + -9x + x10

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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