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Simplifying ln(x + 5) + ln(x + 2) = ln * 18x Reorder the terms: ln(5 + x) + ln(x + 2) = ln * 18x (5 * ln + x * ln) + ln(x + 2) = ln * 18x (5ln + lnx) + ln(x + 2) = ln * 18x Reorder the terms: 5ln + lnx + ln(2 + x) = ln * 18x 5ln + lnx + (2 * ln + x * ln) = ln * 18x 5ln + lnx + (2ln + lnx) = ln * 18x Reorder the terms: 5ln + 2ln + lnx + lnx = ln * 18x Combine like terms: 5ln + 2ln = 7ln 7ln + lnx + lnx = ln * 18x Combine like terms: lnx + lnx = 2lnx 7ln + 2lnx = ln * 18x Reorder the terms for easier multiplication: 7ln + 2lnx = 18ln * x Multiply ln * x 7ln + 2lnx = 18lnx Solving 7ln + 2lnx = 18lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18lnx' to each side of the equation. 7ln + 2lnx + -18lnx = 18lnx + -18lnx Combine like terms: 2lnx + -18lnx = -16lnx 7ln + -16lnx = 18lnx + -18lnx Combine like terms: 18lnx + -18lnx = 0 7ln + -16lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + -16x) = 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 '(7 + -16x)' equal to zero and attempt to solve: Simplifying 7 + -16x = 0 Solving 7 + -16x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -16x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -16x = 0 + -7 -16x = 0 + -7 Combine like terms: 0 + -7 = -7 -16x = -7 Add '16x' to each side of the equation. -16x + 16x = -7 + 16x Combine like terms: -16x + 16x = 0 0 = -7 + 16x Simplifying 0 = -7 + 16x 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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