ln(x+2)=-ln(6x)+ln(17)

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Solution for ln(x+2)=-ln(6x)+ln(17) equation: 


Simplifying
ln(x + 2) = -1ln(6x) + ln(17)

Reorder the terms:
ln(2 + x) = -1ln(6x) + ln(17)
(2 * ln + x * ln) = -1ln(6x) + ln(17)
(2ln + lnx) = -1ln(6x) + ln(17)

Remove parenthesis around (6x)
2ln + lnx = -1ln * 6x + ln(17)

Reorder the terms for easier multiplication:
2ln + lnx = -1 * 6ln * x + ln(17)

Multiply -1 * 6
2ln + lnx = -6ln * x + ln(17)

Multiply ln * x
2ln + lnx = -6lnx + ln(17)

Reorder the terms for easier multiplication:
2ln + lnx = -6lnx + 17ln

Reorder the terms:
2ln + lnx = 17ln + -6lnx

Solving
2ln + lnx = 17ln + -6lnx

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.
2ln + -17ln + lnx = 17ln + -17ln + -6lnx

Combine like terms: 2ln + -17ln = -15ln
-15ln + lnx = 17ln + -17ln + -6lnx

Combine like terms: 17ln + -17ln = 0
-15ln + lnx = 0 + -6lnx
-15ln + lnx = -6lnx

Add '6lnx' to each side of the equation.
-15ln + lnx + 6lnx = -6lnx + 6lnx

Combine like terms: lnx + 6lnx = 7lnx
-15ln + 7lnx = -6lnx + 6lnx

Combine like terms: -6lnx + 6lnx = 0
-15ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-15 + 7x) = 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 '(-15 + 7x)' equal to zero and attempt to solve:

Simplifying
-15 + 7x = 0

Solving
-15 + 7x = 0

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

Add '15' to each side of the equation.
-15 + 15 + 7x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 7x = 0 + 15
7x = 0 + 15

Combine like terms: 0 + 15 = 15
7x = 15

Add '-7x' to each side of the equation.
7x + -7x = 15 + -7x

Combine like terms: 7x + -7x = 0
0 = 15 + -7x

Simplifying
0 = 15 + -7x

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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