ln(x+10)=ln(x-6)+ln(X-1)

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Solution for ln(x+10)=ln(x-6)+ln(X-1) equation: 


Simplifying
ln(x + 10) = ln(x + -6) + ln(X + -1)

Reorder the terms:
ln(10 + x) = ln(x + -6) + ln(X + -1)
(10 * ln + x * ln) = ln(x + -6) + ln(X + -1)
(10ln + lnx) = ln(x + -6) + ln(X + -1)

Reorder the terms:
10ln + lnx = ln(-6 + x) + ln(X + -1)
10ln + lnx = (-6 * ln + x * ln) + ln(X + -1)
10ln + lnx = (-6ln + lnx) + ln(X + -1)

Reorder the terms:
10ln + lnx = -6ln + lnx + ln(-1 + X)
10ln + lnx = -6ln + lnx + (-1 * ln + X * ln)
10ln + lnx = -6ln + lnx + (-1ln + lnX)

Reorder the terms:
10ln + lnx = -6ln + -1ln + lnX + lnx

Combine like terms: -6ln + -1ln = -7ln
10ln + lnx = -7ln + lnX + lnx

Add '-1lnx' to each side of the equation.
10ln + lnx + -1lnx = -7ln + lnX + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
10ln + 0 = -7ln + lnX + lnx + -1lnx
10ln = -7ln + lnX + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
10ln = -7ln + lnX + 0
10ln = -7ln + lnX

Solving
10ln = -7ln + lnX

Solving for variable 'l'.

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

Add '7ln' to each side of the equation.
10ln + 7ln = -7ln + 7ln + lnX

Combine like terms: 10ln + 7ln = 17ln
17ln = -7ln + 7ln + lnX

Combine like terms: -7ln + 7ln = 0
17ln = 0 + lnX
17ln = lnX

Add '-1lnX' to each side of the equation.
17ln + -1lnX = lnX + -1lnX

Combine like terms: lnX + -1lnX = 0
17ln + -1lnX = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(17 + -1X) = 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 '(17 + -1X)' equal to zero and attempt to solve:

Simplifying
17 + -1X = 0

Solving
17 + -1X = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1X = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1X = 0 + -17
-1X = 0 + -17

Combine like terms: 0 + -17 = -17
-1X = -17

Add 'X' to each side of the equation.
-1X + X = -17 + X

Combine like terms: -1X + X = 0
0 = -17 + X

Simplifying
0 = -17 + X

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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