ln(4)+ln(x-6)=ln(15)

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Solution for ln(4)+ln(x-6)=ln(15) equation: 


Simplifying
ln(4) + ln(x + -6) = ln(15)

Reorder the terms for easier multiplication:
4ln + ln(x + -6) = ln(15)

Reorder the terms:
4ln + ln(-6 + x) = ln(15)
4ln + (-6 * ln + x * ln) = ln(15)
4ln + (-6ln + lnx) = ln(15)

Combine like terms: 4ln + -6ln = -2ln
-2ln + lnx = ln(15)

Reorder the terms for easier multiplication:
-2ln + lnx = 15ln

Solving
-2ln + lnx = 15ln

Solving for variable 'l'.

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

Add '-15ln' to each side of the equation.
-2ln + -15ln + lnx = 15ln + -15ln

Combine like terms: -2ln + -15ln = -17ln
-17ln + lnx = 15ln + -15ln

Combine like terms: 15ln + -15ln = 0
-17ln + lnx = 0

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

Simplifying
-17 + x = 0

Solving
-17 + x = 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 + x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + x = 0 + 17
x = 0 + 17

Combine like terms: 0 + 17 = 17
x = 17

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

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

Simplifying
0 = 17 + -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.

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