ln(x+6)+2ln(x)=ln(5)+ln(2)

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Solution for ln(x+6)+2ln(x)=ln(5)+ln(2) equation: 


Simplifying
ln(x + 6) + 2ln(x) = ln(5) + ln(2)

Reorder the terms:
ln(6 + x) + 2ln(x) = ln(5) + ln(2)
(6 * ln + x * ln) + 2ln(x) = ln(5) + ln(2)
(6ln + lnx) + 2ln(x) = ln(5) + ln(2)

Multiply ln * x
6ln + lnx + 2lnx = ln(5) + ln(2)

Combine like terms: lnx + 2lnx = 3lnx
6ln + 3lnx = ln(5) + ln(2)

Reorder the terms for easier multiplication:
6ln + 3lnx = 5ln + ln(2)

Reorder the terms for easier multiplication:
6ln + 3lnx = 5ln + 2ln

Combine like terms: 5ln + 2ln = 7ln
6ln + 3lnx = 7ln

Solving
6ln + 3lnx = 7ln

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.
6ln + -7ln + 3lnx = 7ln + -7ln

Combine like terms: 6ln + -7ln = -1ln
-1ln + 3lnx = 7ln + -7ln

Combine like terms: 7ln + -7ln = 0
-1ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 3x) = 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 '(-1 + 3x)' equal to zero and attempt to solve:

Simplifying
-1 + 3x = 0

Solving
-1 + 3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3x = 0 + 1
3x = 0 + 1

Combine like terms: 0 + 1 = 1
3x = 1

Add '-3x' to each side of the equation.
3x + -3x = 1 + -3x

Combine like terms: 3x + -3x = 0
0 = 1 + -3x

Simplifying
0 = 1 + -3x

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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