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Simplifying (x + 3) * ln(5) = (7x) * ln(7) Reorder the terms: (3 + x) * ln(5) = (7x) * ln(7) Reorder the terms for easier multiplication: 5ln(3 + x) = (7x) * ln(7) (3 * 5ln + x * 5ln) = (7x) * ln(7) (15ln + 5lnx) = (7x) * ln(7) Remove parenthesis around (7x) 15ln + 5lnx = 7x * ln(7) Reorder the terms for easier multiplication: 15ln + 5lnx = 7 * 7x * ln Multiply 7 * 7 15ln + 5lnx = 49x * ln Multiply x * ln 15ln + 5lnx = 49lnx Solving 15ln + 5lnx = 49lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-49lnx' to each side of the equation. 15ln + 5lnx + -49lnx = 49lnx + -49lnx Combine like terms: 5lnx + -49lnx = -44lnx 15ln + -44lnx = 49lnx + -49lnx Combine like terms: 49lnx + -49lnx = 0 15ln + -44lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(15 + -44x) = 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 + -44x)' equal to zero and attempt to solve: Simplifying 15 + -44x = 0 Solving 15 + -44x = 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 + -44x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -44x = 0 + -15 -44x = 0 + -15 Combine like terms: 0 + -15 = -15 -44x = -15 Add '44x' to each side of the equation. -44x + 44x = -15 + 44x Combine like terms: -44x + 44x = 0 0 = -15 + 44x Simplifying 0 = -15 + 44x 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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