ln(19)=ln(2)+ln(x+6)

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Solution for ln(19)=ln(2)+ln(x+6) equation: 


Simplifying
ln(19) = ln(2) + ln(x + 6)

Reorder the terms for easier multiplication:
19ln = ln(2) + ln(x + 6)

Reorder the terms for easier multiplication:
19ln = 2ln + ln(x + 6)

Reorder the terms:
19ln = 2ln + ln(6 + x)
19ln = 2ln + (6 * ln + x * ln)
19ln = 2ln + (6ln + lnx)

Combine like terms: 2ln + 6ln = 8ln
19ln = 8ln + lnx

Solving
19ln = 8ln + lnx

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
19ln + -8ln = 8ln + -8ln + lnx

Combine like terms: 19ln + -8ln = 11ln
11ln = 8ln + -8ln + lnx

Combine like terms: 8ln + -8ln = 0
11ln = 0 + lnx
11ln = lnx

Add '-1lnx' to each side of the equation.
11ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
11ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(11 + -1x) = 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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Add 'x' to each side of the equation.
-1x + x = -11 + x

Combine like terms: -1x + x = 0
0 = -11 + x

Simplifying
0 = -11 + x

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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