2ln(x+2)-ln(8x+1)=0

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Solution for 2ln(x+2)-ln(8x+1)=0 equation: 


Simplifying
2ln(x + 2) + -1ln(8x + 1) = 0

Reorder the terms:
2ln(2 + x) + -1ln(8x + 1) = 0
(2 * 2ln + x * 2ln) + -1ln(8x + 1) = 0
(4ln + 2lnx) + -1ln(8x + 1) = 0

Reorder the terms:
4ln + 2lnx + -1ln(1 + 8x) = 0
4ln + 2lnx + (1 * -1ln + 8x * -1ln) = 0
4ln + 2lnx + (-1ln + -8lnx) = 0

Reorder the terms:
4ln + -1ln + 2lnx + -8lnx = 0

Combine like terms: 4ln + -1ln = 3ln
3ln + 2lnx + -8lnx = 0

Combine like terms: 2lnx + -8lnx = -6lnx
3ln + -6lnx = 0

Solving
3ln + -6lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(1 + -2x) = 0

Ignore the factor 3.

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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Add '2x' to each side of the equation.
-2x + 2x = -1 + 2x

Combine like terms: -2x + 2x = 0
0 = -1 + 2x

Simplifying
0 = -1 + 2x

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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