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Simplifying ln(x2 + 10x + 1) = ln(7x + 1) + ln(x) Reorder the terms: ln(1 + 10x + x2) = ln(7x + 1) + ln(x) (1 * ln + 10x * ln + x2 * ln) = ln(7x + 1) + ln(x) (1ln + 10lnx + lnx2) = ln(7x + 1) + ln(x) Reorder the terms: 1ln + 10lnx + lnx2 = ln(1 + 7x) + ln(x) 1ln + 10lnx + lnx2 = (1 * ln + 7x * ln) + ln(x) 1ln + 10lnx + lnx2 = (1ln + 7lnx) + ln(x) Multiply ln * x 1ln + 10lnx + lnx2 = 1ln + 7lnx + lnx Combine like terms: 7lnx + lnx = 8lnx 1ln + 10lnx + lnx2 = 1ln + 8lnx Add '-1ln' to each side of the equation. 1ln + 10lnx + -1ln + lnx2 = 1ln + -1ln + 8lnx Reorder the terms: 1ln + -1ln + 10lnx + lnx2 = 1ln + -1ln + 8lnx Combine like terms: 1ln + -1ln = 0 0 + 10lnx + lnx2 = 1ln + -1ln + 8lnx 10lnx + lnx2 = 1ln + -1ln + 8lnx Combine like terms: 1ln + -1ln = 0 10lnx + lnx2 = 0 + 8lnx 10lnx + lnx2 = 8lnx Solving 10lnx + lnx2 = 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8lnx' to each side of the equation. 10lnx + -8lnx + lnx2 = 8lnx + -8lnx Combine like terms: 10lnx + -8lnx = 2lnx 2lnx + lnx2 = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 2lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'lnx'. lnx(2 + 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 '(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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