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Simplifying ln(8x3) = 3ln(2x) Remove parenthesis around (8x3) ln * 8x3 = 3ln(2x) Reorder the terms for easier multiplication: 8ln * x3 = 3ln(2x) Multiply ln * x3 8lnx3 = 3ln(2x) Remove parenthesis around (2x) 8lnx3 = 3ln * 2x Reorder the terms for easier multiplication: 8lnx3 = 3 * 2ln * x Multiply 3 * 2 8lnx3 = 6ln * x Multiply ln * x 8lnx3 = 6lnx Solving 8lnx3 = 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6lnx' to each side of the equation. -6lnx + 8lnx3 = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -6lnx + 8lnx3 = 0 Factor out the Greatest Common Factor (GCF), '2lnx'. 2lnx(-3 + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3 + 4x2)' equal to zero and attempt to solve: Simplifying -3 + 4x2 = 0 Solving -3 + 4x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 4x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x2 = 0 + 3 4x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4x2 = 3 Add '-4x2' to each side of the equation. 4x2 + -4x2 = 3 + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 = 3 + -4x2 Simplifying 0 = 3 + -4x2 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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