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Simplifying ln(x + 2) = -1ln(6x) + ln(17) Reorder the terms: ln(2 + x) = -1ln(6x) + ln(17) (2 * ln + x * ln) = -1ln(6x) + ln(17) (2ln + lnx) = -1ln(6x) + ln(17) Remove parenthesis around (6x) 2ln + lnx = -1ln * 6x + ln(17) Reorder the terms for easier multiplication: 2ln + lnx = -1 * 6ln * x + ln(17) Multiply -1 * 6 2ln + lnx = -6ln * x + ln(17) Multiply ln * x 2ln + lnx = -6lnx + ln(17) Reorder the terms for easier multiplication: 2ln + lnx = -6lnx + 17ln Reorder the terms: 2ln + lnx = 17ln + -6lnx Solving 2ln + lnx = 17ln + -6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-17ln' to each side of the equation. 2ln + -17ln + lnx = 17ln + -17ln + -6lnx Combine like terms: 2ln + -17ln = -15ln -15ln + lnx = 17ln + -17ln + -6lnx Combine like terms: 17ln + -17ln = 0 -15ln + lnx = 0 + -6lnx -15ln + lnx = -6lnx Add '6lnx' to each side of the equation. -15ln + lnx + 6lnx = -6lnx + 6lnx Combine like terms: lnx + 6lnx = 7lnx -15ln + 7lnx = -6lnx + 6lnx Combine like terms: -6lnx + 6lnx = 0 -15ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-15 + 7x) = 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 '(-15 + 7x)' equal to zero and attempt to solve: Simplifying -15 + 7x = 0 Solving -15 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 7x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 7x = 0 + 15 7x = 0 + 15 Combine like terms: 0 + 15 = 15 7x = 15 Add '-7x' to each side of the equation. 7x + -7x = 15 + -7x Combine like terms: 7x + -7x = 0 0 = 15 + -7x Simplifying 0 = 15 + -7x 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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