ln(x+6)+ln(x)=ln(15)

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Solution for ln(x+6)+ln(x)=ln(15) equation: 


Simplifying
ln(x + 6) + ln(x) = ln(15)

Reorder the terms:
ln(6 + x) + ln(x) = ln(15)
(6 * ln + x * ln) + ln(x) = ln(15)
(6ln + lnx) + ln(x) = ln(15)

Multiply ln * x
6ln + lnx + lnx = ln(15)

Combine like terms: lnx + lnx = 2lnx
6ln + 2lnx = ln(15)

Reorder the terms for easier multiplication:
6ln + 2lnx = 15ln

Solving
6ln + 2lnx = 15ln

Solving for variable 'l'.

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

Add '-15ln' to each side of the equation.
6ln + -15ln + 2lnx = 15ln + -15ln

Combine like terms: 6ln + -15ln = -9ln
-9ln + 2lnx = 15ln + -15ln

Combine like terms: 15ln + -15ln = 0
-9ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-9 + 2x) = 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 '(-9 + 2x)' equal to zero and attempt to solve:

Simplifying
-9 + 2x = 0

Solving
-9 + 2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + 2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2x = 0 + 9
2x = 0 + 9

Combine like terms: 0 + 9 = 9
2x = 9

Add '-2x' to each side of the equation.
2x + -2x = 9 + -2x

Combine like terms: 2x + -2x = 0
0 = 9 + -2x

Simplifying
0 = 9 + -2x

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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