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

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


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

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

Remove parenthesis around (2x)
lnx + ln * 2x = ln(8)

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

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

Combine like terms: lnx + 2lnx = 3lnx
3lnx = ln(8)

Reorder the terms for easier multiplication:
3lnx = 8ln

Solving
3lnx = 8ln

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.
-8ln + 3lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-8ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-8 + 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 '(-8 + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + 3x = 0

Solving
-8 + 3x = 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 + 3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8

Combine like terms: 0 + 8 = 8
3x = 8

Add '-3x' to each side of the equation.
3x + -3x = 8 + -3x

Combine like terms: 3x + -3x = 0
0 = 8 + -3x

Simplifying
0 = 8 + -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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