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Simplifying ln(x2 + 21) = ln(10x) Reorder the terms: ln(21 + x2) = ln(10x) (21 * ln + x2 * ln) = ln(10x) (21ln + lnx2) = ln(10x) Remove parenthesis around (10x) 21ln + lnx2 = ln * 10x Reorder the terms for easier multiplication: 21ln + lnx2 = 10ln * x Multiply ln * x 21ln + lnx2 = 10lnx Solving 21ln + lnx2 = 10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10lnx' to each side of the equation. 21ln + -10lnx + lnx2 = 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 21ln + -10lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(21 + -10x + x2) = 0 Factor a trinomial. ln((3 + -1x)(7 + -1x)) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + x 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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