ln(x)+ln(2x)=ln(3)

Solution for ln(x)+ln(2x)=ln(3) equation:

Simplifying
ln(x) + ln(2x) = ln(3)

Multiply ln * x
lnx + ln(2x) = ln(3)

Remove parenthesis around (2x)
lnx + ln * 2x = ln(3)

Reorder the terms for easier multiplication:
lnx + 2ln * x = ln(3)

Multiply ln * x
lnx + 2lnx = ln(3)

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

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

Solving
3lnx = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-3ln + 3lnx = 3ln + -3ln

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

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(-1 + x) = 0

Ignore the factor 3.
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 '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

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

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

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

Simplifying
0 = 1 + -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.