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Simplifying ln(3x + 4) + lnx = ln(17x + 10) Reorder the terms: ln(4 + 3x) + lnx = ln(17x + 10) (4 * ln + 3x * ln) + lnx = ln(17x + 10) (4ln + 3lnx) + lnx = ln(17x + 10) Combine like terms: 3lnx + lnx = 4lnx 4ln + 4lnx = ln(17x + 10) Reorder the terms: 4ln + 4lnx = ln(10 + 17x) 4ln + 4lnx = (10 * ln + 17x * ln) 4ln + 4lnx = (10ln + 17lnx) Solving 4ln + 4lnx = 10ln + 17lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. 4ln + -10ln + 4lnx = 10ln + -10ln + 17lnx Combine like terms: 4ln + -10ln = -6ln -6ln + 4lnx = 10ln + -10ln + 17lnx Combine like terms: 10ln + -10ln = 0 -6ln + 4lnx = 0 + 17lnx -6ln + 4lnx = 17lnx Add '-17lnx' to each side of the equation. -6ln + 4lnx + -17lnx = 17lnx + -17lnx Combine like terms: 4lnx + -17lnx = -13lnx -6ln + -13lnx = 17lnx + -17lnx Combine like terms: 17lnx + -17lnx = 0 -6ln + -13lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(6 + 13x) = 0 Ignore the factor -1.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 '(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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