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Simplifying ln(3)(2x + 1) = ln(15)(-3x + 2) Reorder the terms: ln * 3(1 + 2x) = ln(15)(-3x + 2) Reorder the terms for easier multiplication: 3ln(1 + 2x) = ln(15)(-3x + 2) (1 * 3ln + 2x * 3ln) = ln(15)(-3x + 2) (3ln + 6lnx) = ln(15)(-3x + 2) Reorder the terms: 3ln + 6lnx = ln * 15(2 + -3x) Reorder the terms for easier multiplication: 3ln + 6lnx = 15ln(2 + -3x) 3ln + 6lnx = (2 * 15ln + -3x * 15ln) 3ln + 6lnx = (30ln + -45lnx) Solving 3ln + 6lnx = 30ln + -45lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-30ln' to each side of the equation. 3ln + -30ln + 6lnx = 30ln + -30ln + -45lnx Combine like terms: 3ln + -30ln = -27ln -27ln + 6lnx = 30ln + -30ln + -45lnx Combine like terms: 30ln + -30ln = 0 -27ln + 6lnx = 0 + -45lnx -27ln + 6lnx = -45lnx Add '45lnx' to each side of the equation. -27ln + 6lnx + 45lnx = -45lnx + 45lnx Combine like terms: 6lnx + 45lnx = 51lnx -27ln + 51lnx = -45lnx + 45lnx Combine like terms: -45lnx + 45lnx = 0 -27ln + 51lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-9 + 17x) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 '(-9 + 17x)' equal to zero and attempt to solve: Simplifying -9 + 17x = 0 Solving -9 + 17x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 17x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 17x = 0 + 9 17x = 0 + 9 Combine like terms: 0 + 9 = 9 17x = 9 Add '-17x' to each side of the equation. 17x + -17x = 9 + -17x Combine like terms: 17x + -17x = 0 0 = 9 + -17x Simplifying 0 = 9 + -17x 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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