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Simplifying ln(4x + 2) = ln(8) + ln(x) Reorder the terms: ln(2 + 4x) = ln(8) + ln(x) (2 * ln + 4x * ln) = ln(8) + ln(x) (2ln + 4lnx) = ln(8) + ln(x) Reorder the terms for easier multiplication: 2ln + 4lnx = 8ln + ln(x) Multiply ln * x 2ln + 4lnx = 8ln + lnx Solving 2ln + 4lnx = 8ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 2ln + -8ln + 4lnx = 8ln + -8ln + lnx Combine like terms: 2ln + -8ln = -6ln -6ln + 4lnx = 8ln + -8ln + lnx Combine like terms: 8ln + -8ln = 0 -6ln + 4lnx = 0 + lnx -6ln + 4lnx = lnx Add '-1lnx' to each side of the equation. -6ln + 4lnx + -1lnx = lnx + -1lnx Combine like terms: 4lnx + -1lnx = 3lnx -6ln + 3lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -6ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-2 + x) = 0 Ignore the factor 3.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -1x 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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