ln(x-35)+ln(x+180)=3*ln(6)

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Solution for ln(x-35)+ln(x+180)=3*ln(6) equation: 


Simplifying
ln(x + -35) + ln(x + 180) = 3ln(6)

Reorder the terms:
ln(-35 + x) + ln(x + 180) = 3ln(6)
(-35 * ln + x * ln) + ln(x + 180) = 3ln(6)
(-35ln + lnx) + ln(x + 180) = 3ln(6)

Reorder the terms:
-35ln + lnx + ln(180 + x) = 3ln(6)
-35ln + lnx + (180 * ln + x * ln) = 3ln(6)
-35ln + lnx + (180ln + lnx) = 3ln(6)

Reorder the terms:
-35ln + 180ln + lnx + lnx = 3ln(6)

Combine like terms: -35ln + 180ln = 145ln
145ln + lnx + lnx = 3ln(6)

Combine like terms: lnx + lnx = 2lnx
145ln + 2lnx = 3ln(6)

Reorder the terms for easier multiplication:
145ln + 2lnx = 3 * 6ln

Multiply 3 * 6
145ln + 2lnx = 18ln

Solving
145ln + 2lnx = 18ln

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.
145ln + -18ln + 2lnx = 18ln + -18ln

Combine like terms: 145ln + -18ln = 127ln
127ln + 2lnx = 18ln + -18ln

Combine like terms: 18ln + -18ln = 0
127ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(127 + 2x) = 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 '(127 + 2x)' equal to zero and attempt to solve:

Simplifying
127 + 2x = 0

Solving
127 + 2x = 0

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

Add '-127' to each side of the equation.
127 + -127 + 2x = 0 + -127

Combine like terms: 127 + -127 = 0
0 + 2x = 0 + -127
2x = 0 + -127

Combine like terms: 0 + -127 = -127
2x = -127

Add '-2x' to each side of the equation.
2x + -2x = -127 + -2x

Combine like terms: 2x + -2x = 0
0 = -127 + -2x

Simplifying
0 = -127 + -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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