ln(4x+6)+1=7

Solution for ln(4x+6)+1=7 equation:

Simplifying
ln(4x + 6) + 1 = 7

Reorder the terms:
ln(6 + 4x) + 1 = 7
(6 * ln + 4x * ln) + 1 = 7
(6ln + 4lnx) + 1 = 7

Reorder the terms:
1 + 6ln + 4lnx = 7

Solving
1 + 6ln + 4lnx = 7

Solving for variable 'l'.

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

Add '-1' to each side of the equation.
1 + 6ln + -1 + 4lnx = 7 + -1

Reorder the terms:
1 + -1 + 6ln + 4lnx = 7 + -1

Combine like terms: 1 + -1 = 0
0 + 6ln + 4lnx = 7 + -1
6ln + 4lnx = 7 + -1

Combine like terms: 7 + -1 = 6
6ln + 4lnx = 6

Reorder the terms:
-6 + 6ln + 4lnx = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 6ln + 4lnx = 0

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

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

Simplifying
-3 + 3ln + 2lnx = 0

Solving
-3 + 3ln + 2lnx = 0

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

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

Reorder the terms:
-3 + 3 + 3ln + 2lnx = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3ln + 2lnx = 0 + 3
3ln + 2lnx = 0 + 3

Combine like terms: 0 + 3 = 3
3ln + 2lnx = 3

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.