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