ln(x)+ln(x-6)=ln(8x)

Solution for ln(x)+ln(x-6)=ln(8x) equation:

Simplifying
ln(x) + ln(x + -6) = ln(8x)

Multiply ln * x
lnx + ln(x + -6) = ln(8x)

Reorder the terms:
lnx + ln(-6 + x) = ln(8x)
lnx + (-6 * ln + x * ln) = ln(8x)
lnx + (-6ln + lnx) = ln(8x)

Reorder the terms:
-6ln + lnx + lnx = ln(8x)

Combine like terms: lnx + lnx = 2lnx
-6ln + 2lnx = ln(8x)

Remove parenthesis around (8x)
-6ln + 2lnx = ln * 8x

Reorder the terms for easier multiplication:
-6ln + 2lnx = 8ln * x

Multiply ln * x
-6ln + 2lnx = 8lnx

Solving
-6ln + 2lnx = 8lnx

Solving for variable 'l'.

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

Add '-8lnx' to each side of the equation.
-6ln + 2lnx + -8lnx = 8lnx + -8lnx

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

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

Factor out the Greatest Common Factor (GCF), '-6ln'.
-6ln(1 + x) = 0

Ignore the factor -6.
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 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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

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

Simplifying
0 = -1 + -1x

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.