54=6ln(4x+1)

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Solution for 54=6ln(4x+1) equation:


Simplifying
54 = 6ln(4x + 1)

Reorder the terms:
54 = 6ln(1 + 4x)
54 = (1 * 6ln + 4x * 6ln)
54 = (6ln + 24lnx)

Solving
54 = 6ln + 24lnx

Solving for variable 'l'.

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

Add '-6ln' to each side of the equation.
54 + -6ln = 6ln + -6ln + 24lnx

Combine like terms: 6ln + -6ln = 0
54 + -6ln = 0 + 24lnx
54 + -6ln = 24lnx

Add '-24lnx' to each side of the equation.
54 + -6ln + -24lnx = 24lnx + -24lnx

Combine like terms: 24lnx + -24lnx = 0
54 + -6ln + -24lnx = 0

Add '-54' to each side of the equation.
54 + -6ln + -54 + -24lnx = 0 + -54

Reorder the terms:
54 + -54 + -6ln + -24lnx = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -6ln + -24lnx = 0 + -54
-6ln + -24lnx = 0 + -54

Combine like terms: 0 + -54 = -54
-6ln + -24lnx = -54

Reorder the terms:
54 + -6ln + -24lnx = -54 + 54

Combine like terms: -54 + 54 = 0
54 + -6ln + -24lnx = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(9 + -1ln + -4lnx) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(9 + -1ln + -4lnx)' equal to zero and attempt to solve: Simplifying 9 + -1ln + -4lnx = 0 Solving 9 + -1ln + -4lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -1ln + -9 + -4lnx = 0 + -9 Reorder the terms: 9 + -9 + -1ln + -4lnx = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1ln + -4lnx = 0 + -9 -1ln + -4lnx = 0 + -9 Combine like terms: 0 + -9 = -9 -1ln + -4lnx = -9 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.

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