2ln(x)=ln(4)+ln(8+x)

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Solution for 2ln(x)=ln(4)+ln(8+x) equation: 


Simplifying
2ln(x) = ln(4) + ln(8 + x)

Multiply ln * x
2lnx = ln(4) + ln(8 + x)

Reorder the terms for easier multiplication:
2lnx = 4ln + ln(8 + x)
2lnx = 4ln + (8 * ln + x * ln)
2lnx = 4ln + (8ln + lnx)

Combine like terms: 4ln + 8ln = 12ln
2lnx = 12ln + lnx

Solving
2lnx = 12ln + lnx

Solving for variable 'l'.

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

Add '-12ln' to each side of the equation.
-12ln + 2lnx = 12ln + -12ln + lnx

Combine like terms: 12ln + -12ln = 0
-12ln + 2lnx = 0 + lnx
-12ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-12ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-12ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-12ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-12 + x) = 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 '(-12 + x)' equal to zero and attempt to solve:

Simplifying
-12 + x = 0

Solving
-12 + x = 0

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

Add '12' to each side of the equation.
-12 + 12 + x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + x = 0 + 12
x = 0 + 12

Combine like terms: 0 + 12 = 12
x = 12

Add '-1x' to each side of the equation.
x + -1x = 12 + -1x

Combine like terms: x + -1x = 0
0 = 12 + -1x

Simplifying
0 = 12 + -1x

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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