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

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

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

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

Remove parenthesis around (4x)
8ln + ln * 4x = 2

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

Multiply ln * x
8ln + 4lnx = 2

Solving
8ln + 4lnx = 2

Solving for variable 'l'.

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

Reorder the terms:
-2 + 8ln + 4lnx = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 8ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 4ln + 2lnx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 4ln + 2lnx)' equal to zero and attempt to solve:

Simplifying
-1 + 4ln + 2lnx = 0

Solving
-1 + 4ln + 2lnx = 0

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

Add '1' to each side of the equation.
-1 + 4ln + 1 + 2lnx = 0 + 1

Reorder the terms:
-1 + 1 + 4ln + 2lnx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4ln + 2lnx = 0 + 1
4ln + 2lnx = 0 + 1

Combine like terms: 0 + 1 = 1
4ln + 2lnx = 1

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.