ln(x)+ln(x-6)=ln(91)

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Solution for ln(x)+ln(x-6)=ln(91) equation: 


Simplifying
ln(x) + ln(x + -6) = ln(91)

Multiply ln * x
lnx + ln(x + -6) = ln(91)

Reorder the terms:
lnx + ln(-6 + x) = ln(91)
lnx + (-6 * ln + x * ln) = ln(91)
lnx + (-6ln + lnx) = ln(91)

Reorder the terms:
-6ln + lnx + lnx = ln(91)

Combine like terms: lnx + lnx = 2lnx
-6ln + 2lnx = ln(91)

Reorder the terms for easier multiplication:
-6ln + 2lnx = 91ln

Solving
-6ln + 2lnx = 91ln

Solving for variable 'l'.

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

Add '-91ln' to each side of the equation.
-6ln + -91ln + 2lnx = 91ln + -91ln

Combine like terms: -6ln + -91ln = -97ln
-97ln + 2lnx = 91ln + -91ln

Combine like terms: 91ln + -91ln = 0
-97ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-97 + 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 '(-97 + 2x)' equal to zero and attempt to solve:

Simplifying
-97 + 2x = 0

Solving
-97 + 2x = 0

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

Add '97' to each side of the equation.
-97 + 97 + 2x = 0 + 97

Combine like terms: -97 + 97 = 0
0 + 2x = 0 + 97
2x = 0 + 97

Combine like terms: 0 + 97 = 97
2x = 97

Add '-2x' to each side of the equation.
2x + -2x = 97 + -2x

Combine like terms: 2x + -2x = 0
0 = 97 + -2x

Simplifying
0 = 97 + -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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