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Simplifying ln(27x + 5) = ln(14) Reorder the terms: ln(5 + 27x) = ln(14) (5 * ln + 27x * ln) = ln(14) (5ln + 27lnx) = ln(14) Reorder the terms for easier multiplication: 5ln + 27lnx = 14ln Solving 5ln + 27lnx = 14ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. 5ln + -14ln + 27lnx = 14ln + -14ln Combine like terms: 5ln + -14ln = -9ln -9ln + 27lnx = 14ln + -14ln Combine like terms: 14ln + -14ln = 0 -9ln + 27lnx = 0 Factor out the Greatest Common Factor (GCF), '9ln'. 9ln(-1 + 3x) = 0 Ignore the factor 9.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 '(-1 + 3x)' equal to zero and attempt to solve: Simplifying -1 + 3x = 0 Solving -1 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3x = 0 + 1 3x = 0 + 1 Combine like terms: 0 + 1 = 1 3x = 1 Add '-3x' to each side of the equation. 3x + -3x = 1 + -3x Combine like terms: 3x + -3x = 0 0 = 1 + -3x Simplifying 0 = 1 + -3x 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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