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Simplifying 3ln(x) + -4 = ln(6x3) + 2 Multiply ln * x 3lnx + -4 = ln(6x3) + 2 Reorder the terms: -4 + 3lnx = ln(6x3) + 2 Remove parenthesis around (6x3) -4 + 3lnx = ln * 6x3 + 2 Reorder the terms for easier multiplication: -4 + 3lnx = 6ln * x3 + 2 Multiply ln * x3 -4 + 3lnx = 6lnx3 + 2 Reorder the terms: -4 + 3lnx = 2 + 6lnx3 Solving -4 + 3lnx = 2 + 6lnx3 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6lnx3' to each side of the equation. -4 + 3lnx + -6lnx3 = 2 + 6lnx3 + -6lnx3 Combine like terms: 6lnx3 + -6lnx3 = 0 -4 + 3lnx + -6lnx3 = 2 + 0 -4 + 3lnx + -6lnx3 = 2 Add '4' to each side of the equation. -4 + 3lnx + 4 + -6lnx3 = 2 + 4 Reorder the terms: -4 + 4 + 3lnx + -6lnx3 = 2 + 4 Combine like terms: -4 + 4 = 0 0 + 3lnx + -6lnx3 = 2 + 4 3lnx + -6lnx3 = 2 + 4 Combine like terms: 2 + 4 = 6 3lnx + -6lnx3 = 6 Reorder the terms: -6 + 3lnx + -6lnx3 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 3lnx + -6lnx3 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + lnx + -2lnx3) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + lnx + -2lnx3)' equal to zero and attempt to solve: Simplifying -2 + lnx + -2lnx3 = 0 Solving -2 + lnx + -2lnx3 = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + lnx + 2 + -2lnx3 = 0 + 2 Reorder the terms: -2 + 2 + lnx + -2lnx3 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + lnx + -2lnx3 = 0 + 2 lnx + -2lnx3 = 0 + 2 Combine like terms: 0 + 2 = 2 lnx + -2lnx3 = 2 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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