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Simplifying ln(8x) + -1ln(4x2) = 2ln(x) Remove parenthesis around (8x) ln * 8x + -1ln(4x2) = 2ln(x) Reorder the terms for easier multiplication: 8ln * x + -1ln(4x2) = 2ln(x) Multiply ln * x 8lnx + -1ln(4x2) = 2ln(x) Remove parenthesis around (4x2) 8lnx + -1ln * 4x2 = 2ln(x) Reorder the terms for easier multiplication: 8lnx + -1 * 4ln * x2 = 2ln(x) Multiply -1 * 4 8lnx + -4ln * x2 = 2ln(x) Multiply ln * x2 8lnx + -4lnx2 = 2ln(x) Multiply ln * x 8lnx + -4lnx2 = 2lnx Solving 8lnx + -4lnx2 = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. 8lnx + -2lnx + -4lnx2 = 2lnx + -2lnx Combine like terms: 8lnx + -2lnx = 6lnx 6lnx + -4lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 6lnx + -4lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2lnx'. 2lnx(3 + -2x) = 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 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Add '2x' to each side of the equation. -2x + 2x = -3 + 2x Combine like terms: -2x + 2x = 0 0 = -3 + 2x Simplifying 0 = -3 + 2x 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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