ln(x)+ln(x-6)=Ln(10)

Solution for ln(x)+ln(x-6)=Ln(10) equation:

Simplifying
ln(x) + ln(x + -6) = Ln(10)

Multiply ln * x
lnx + ln(x + -6) = Ln(10)

Reorder the terms:
lnx + ln(-6 + x) = Ln(10)
lnx + (-6 * ln + x * ln) = Ln(10)
lnx + (-6ln + lnx) = Ln(10)

Reorder the terms:
-6ln + lnx + lnx = Ln(10)

Combine like terms: lnx + lnx = 2lnx
-6ln + 2lnx = Ln(10)

Reorder the terms for easier multiplication:
-6ln + 2lnx = 10nL

Solving
-6ln + 2lnx = 10nL

Solving for variable 'l'.

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

Combine like terms: 10nL + -10nL = 0
-6ln + 2lnx + -10nL = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(-3l + lx + -5L) = 0

Ignore the factor 2.
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 + -5L)' equal to zero and attempt to solve:

Simplifying
-3l + lx + -5L = 0

Reorder the terms:
-5L + -3l + lx = 0

Solving
-5L + -3l + lx = 0

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

Add '5L' to each side of the equation.
-5L + -3l + 5L + lx = 0 + 5L

Reorder the terms:
-5L + 5L + -3l + lx = 0 + 5L

Combine like terms: -5L + 5L = 0
0 + -3l + lx = 0 + 5L
-3l + lx = 0 + 5L
Remove the zero:
-3l + lx = 5L

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.