48=18+5ln(4x+1)

Solution for 48=18+5ln(4x+1) equation:

Simplifying
48 = 18 + 5ln(4x + 1)

Reorder the terms:
48 = 18 + 5ln(1 + 4x)
48 = 18 + (1 * 5ln + 4x * 5ln)
48 = 18 + (5ln + 20lnx)

Solving
48 = 18 + 5ln + 20lnx

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
48 + -5ln = 18 + 5ln + -5ln + 20lnx

Combine like terms: 5ln + -5ln = 0
48 + -5ln = 18 + 0 + 20lnx
48 + -5ln = 18 + 20lnx

Add '-20lnx' to each side of the equation.
48 + -5ln + -20lnx = 18 + 20lnx + -20lnx

Combine like terms: 20lnx + -20lnx = 0
48 + -5ln + -20lnx = 18 + 0
48 + -5ln + -20lnx = 18

Add '-48' to each side of the equation.
48 + -5ln + -48 + -20lnx = 18 + -48

Reorder the terms:
48 + -48 + -5ln + -20lnx = 18 + -48

Combine like terms: 48 + -48 = 0
0 + -5ln + -20lnx = 18 + -48
-5ln + -20lnx = 18 + -48

Combine like terms: 18 + -48 = -30
-5ln + -20lnx = -30

Reorder the terms:
30 + -5ln + -20lnx = -30 + 30

Combine like terms: -30 + 30 = 0
30 + -5ln + -20lnx = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -1ln + -4lnx) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + -1ln + -4lnx)' equal to zero and attempt to solve:

Simplifying
6 + -1ln + -4lnx = 0

Solving
6 + -1ln + -4lnx = 0

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

Add '-6' to each side of the equation.
6 + -1ln + -6 + -4lnx = 0 + -6

Reorder the terms:
6 + -6 + -1ln + -4lnx = 0 + -6

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

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

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.