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Simplifying ln(3 + -1x) = ln(x + 2) + 2ln(10) (3 * ln + -1x * ln) = ln(x + 2) + 2ln(10) (3ln + -1lnx) = ln(x + 2) + 2ln(10) Reorder the terms: 3ln + -1lnx = ln(2 + x) + 2ln(10) 3ln + -1lnx = (2 * ln + x * ln) + 2ln(10) 3ln + -1lnx = (2ln + lnx) + 2ln(10) Reorder the terms for easier multiplication: 3ln + -1lnx = 2ln + lnx + 2 * 10ln Multiply 2 * 10 3ln + -1lnx = 2ln + lnx + 20ln Reorder the terms: 3ln + -1lnx = 2ln + 20ln + lnx Combine like terms: 2ln + 20ln = 22ln 3ln + -1lnx = 22ln + lnx Solving 3ln + -1lnx = 22ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-22ln' to each side of the equation. 3ln + -22ln + -1lnx = 22ln + -22ln + lnx Combine like terms: 3ln + -22ln = -19ln -19ln + -1lnx = 22ln + -22ln + lnx Combine like terms: 22ln + -22ln = 0 -19ln + -1lnx = 0 + lnx -19ln + -1lnx = lnx Add '-1lnx' to each side of the equation. -19ln + -1lnx + -1lnx = lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx -19ln + -2lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -19ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(19 + 2x) = 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 '(19 + 2x)' equal to zero and attempt to solve: Simplifying 19 + 2x = 0 Solving 19 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 2x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 2x = 0 + -19 2x = 0 + -19 Combine like terms: 0 + -19 = -19 2x = -19 Add '-2x' to each side of the equation. 2x + -2x = -19 + -2x Combine like terms: 2x + -2x = 0 0 = -19 + -2x Simplifying 0 = -19 + -2x 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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