ln(4x)+ln(6x^2)=10

Solution for ln(4x)+ln(6x^2)=10 equation:

Simplifying
ln(4x) + ln(6x2) = 10

Remove parenthesis around (4x)
ln * 4x + ln(6x2) = 10

Reorder the terms for easier multiplication:
4ln * x + ln(6x2) = 10

Multiply ln * x
4lnx + ln(6x2) = 10

Remove parenthesis around (6x2)
4lnx + ln * 6x2 = 10

Reorder the terms for easier multiplication:
4lnx + 6ln * x2 = 10

Multiply ln * x2
4lnx + 6lnx2 = 10

Solving
4lnx + 6lnx2 = 10

Solving for variable 'l'.

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

Reorder the terms:
-10 + 4lnx + 6lnx2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 4lnx + 6lnx2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 2lnx + 3lnx2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 2lnx + 3lnx2)' equal to zero and attempt to solve:

Simplifying
-5 + 2lnx + 3lnx2 = 0

Solving
-5 + 2lnx + 3lnx2 = 0

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

Add '5' to each side of the equation.
-5 + 2lnx + 5 + 3lnx2 = 0 + 5

Reorder the terms:
-5 + 5 + 2lnx + 3lnx2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2lnx + 3lnx2 = 0 + 5
2lnx + 3lnx2 = 0 + 5

Combine like terms: 0 + 5 = 5
2lnx + 3lnx2 = 5

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.