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Simplifying ln(7) + ln(x) = ln(x2) + ln(12) Reorder the terms for easier multiplication: 7ln + ln(x) = ln(x2) + ln(12) Multiply ln * x 7ln + lnx = ln(x2) + ln(12) Multiply ln * x2 7ln + lnx = lnx2 + ln(12) Reorder the terms for easier multiplication: 7ln + lnx = lnx2 + 12ln Reorder the terms: 7ln + lnx = 12ln + lnx2 Solving 7ln + lnx = 12ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 7ln + -12ln + lnx = 12ln + -12ln + lnx2 Combine like terms: 7ln + -12ln = -5ln -5ln + lnx = 12ln + -12ln + lnx2 Combine like terms: 12ln + -12ln = 0 -5ln + lnx = 0 + lnx2 -5ln + lnx = lnx2 Add '-1lnx2' to each side of the equation. -5ln + lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -5ln + lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-5 + x + -1x2) = 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 '(-5 + x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + x + -1x2 = 0 Solving -5 + x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + x + 5 + -1x2 = 0 + 5 Reorder the terms: -5 + 5 + x + -1x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x + -1x2 = 0 + 5 x + -1x2 = 0 + 5 Combine like terms: 0 + 5 = 5 x + -1x2 = 5 Add '-1x' to each side of the equation. x + -1x + -1x2 = 5 + -1x Combine like terms: x + -1x = 0 0 + -1x2 = 5 + -1x -1x2 = 5 + -1x Add 'x2' to each side of the equation. -1x2 + x2 = 5 + -1x + x2 Combine like terms: -1x2 + x2 = 0 0 = 5 + -1x + x2 Simplifying 0 = 5 + -1x + x2 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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