ln(5)+ln(x+6)=ln(17)

Solution for ln(5)+ln(x+6)=ln(17) equation:

Simplifying
ln(5) + ln(x + 6) = ln(17)

Reorder the terms for easier multiplication:
5ln + ln(x + 6) = ln(17)

Reorder the terms:
5ln + ln(6 + x) = ln(17)
5ln + (6 * ln + x * ln) = ln(17)
5ln + (6ln + lnx) = ln(17)

Combine like terms: 5ln + 6ln = 11ln
11ln + lnx = ln(17)

Reorder the terms for easier multiplication:
11ln + lnx = 17ln

Solving
11ln + lnx = 17ln

Solving for variable 'l'.

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

Add '-17ln' to each side of the equation.
11ln + -17ln + lnx = 17ln + -17ln

Combine like terms: 11ln + -17ln = -6ln
-6ln + lnx = 17ln + -17ln

Combine like terms: 17ln + -17ln = 0
-6ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-6 + 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 '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Add '-1x' to each side of the equation.
x + -1x = 6 + -1x

Combine like terms: x + -1x = 0
0 = 6 + -1x

Simplifying
0 = 6 + -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.