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Simplifying ln(2x) + ln(8) = ln(32) Remove parenthesis around (2x) ln * 2x + ln(8) = ln(32) Reorder the terms for easier multiplication: 2ln * x + ln(8) = ln(32) Multiply ln * x 2lnx + ln(8) = ln(32) Reorder the terms for easier multiplication: 2lnx + 8ln = ln(32) Reorder the terms: 8ln + 2lnx = ln(32) Reorder the terms for easier multiplication: 8ln + 2lnx = 32ln Solving 8ln + 2lnx = 32ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32ln' to each side of the equation. 8ln + -32ln + 2lnx = 32ln + -32ln Combine like terms: 8ln + -32ln = -24ln -24ln + 2lnx = 32ln + -32ln Combine like terms: 32ln + -32ln = 0 -24ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-12 + x) = 0 Ignore the factor 2.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 '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Add '-1x' to each side of the equation. x + -1x = 12 + -1x Combine like terms: x + -1x = 0 0 = 12 + -1x Simplifying 0 = 12 + -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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