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Simplifying ln(15x + 2) = 2ln * x + ln * 8 Reorder the terms: ln(2 + 15x) = 2ln * x + ln * 8 (2 * ln + 15x * ln) = 2ln * x + ln * 8 (2ln + 15lnx) = 2ln * x + ln * 8 Multiply ln * x 2ln + 15lnx = 2lnx + ln * 8 Reorder the terms for easier multiplication: 2ln + 15lnx = 2lnx + 8ln Reorder the terms: 2ln + 15lnx = 8ln + 2lnx Solving 2ln + 15lnx = 8ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 2ln + -8ln + 15lnx = 8ln + -8ln + 2lnx Combine like terms: 2ln + -8ln = -6ln -6ln + 15lnx = 8ln + -8ln + 2lnx Combine like terms: 8ln + -8ln = 0 -6ln + 15lnx = 0 + 2lnx -6ln + 15lnx = 2lnx Add '-2lnx' to each side of the equation. -6ln + 15lnx + -2lnx = 2lnx + -2lnx Combine like terms: 15lnx + -2lnx = 13lnx -6ln + 13lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -6ln + 13lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-6 + 13x) = 0Subproblem 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 '(-6 + 13x)' equal to zero and attempt to solve: Simplifying -6 + 13x = 0 Solving -6 + 13x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 13x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 13x = 0 + 6 13x = 0 + 6 Combine like terms: 0 + 6 = 6 13x = 6 Add '-13x' to each side of the equation. 13x + -13x = 6 + -13x Combine like terms: 13x + -13x = 0 0 = 6 + -13x Simplifying 0 = 6 + -13x 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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