ln(6)+ln(x+2)=ln(14x)

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Solution for ln(6)+ln(x+2)=ln(14x) equation: 


Simplifying
ln(6) + ln(x + 2) = ln(14x)

Reorder the terms for easier multiplication:
6ln + ln(x + 2) = ln(14x)

Reorder the terms:
6ln + ln(2 + x) = ln(14x)
6ln + (2 * ln + x * ln) = ln(14x)
6ln + (2ln + lnx) = ln(14x)

Combine like terms: 6ln + 2ln = 8ln
8ln + lnx = ln(14x)

Remove parenthesis around (14x)
8ln + lnx = ln * 14x

Reorder the terms for easier multiplication:
8ln + lnx = 14ln * x

Multiply ln * x
8ln + lnx = 14lnx

Solving
8ln + lnx = 14lnx

Solving for variable 'l'.

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

Add '-14lnx' to each side of the equation.
8ln + lnx + -14lnx = 14lnx + -14lnx

Combine like terms: lnx + -14lnx = -13lnx
8ln + -13lnx = 14lnx + -14lnx

Combine like terms: 14lnx + -14lnx = 0
8ln + -13lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(8 + -13x) = 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 '(8 + -13x)' equal to zero and attempt to solve:

Simplifying
8 + -13x = 0

Solving
8 + -13x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -13x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -13x = 0 + -8
-13x = 0 + -8

Combine like terms: 0 + -8 = -8
-13x = -8

Add '13x' to each side of the equation.
-13x + 13x = -8 + 13x

Combine like terms: -13x + 13x = 0
0 = -8 + 13x

Simplifying
0 = -8 + 13x

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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