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Simplifying ln(3x2) = 2ln(3x) Remove parenthesis around (3x2) ln * 3x2 = 2ln(3x) Reorder the terms for easier multiplication: 3ln * x2 = 2ln(3x) Multiply ln * x2 3lnx2 = 2ln(3x) Remove parenthesis around (3x) 3lnx2 = 2ln * 3x Reorder the terms for easier multiplication: 3lnx2 = 2 * 3ln * x Multiply 2 * 3 3lnx2 = 6ln * x Multiply ln * x 3lnx2 = 6lnx Solving 3lnx2 = 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 + 3lnx2 = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -6lnx + 3lnx2 = 0 Factor out the Greatest Common Factor (GCF), '3lnx'. 3lnx(-2 + x) = 0 Ignore the factor 3.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -1x 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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