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Simplifying ln(x) + ln(7x + 8) = ln(2x + 1) Multiply ln * x lnx + ln(7x + 8) = ln(2x + 1) Reorder the terms: lnx + ln(8 + 7x) = ln(2x + 1) lnx + (8 * ln + 7x * ln) = ln(2x + 1) lnx + (8ln + 7lnx) = ln(2x + 1) Reorder the terms: 8ln + lnx + 7lnx = ln(2x + 1) Combine like terms: lnx + 7lnx = 8lnx 8ln + 8lnx = ln(2x + 1) Reorder the terms: 8ln + 8lnx = ln(1 + 2x) 8ln + 8lnx = (1 * ln + 2x * ln) 8ln + 8lnx = (1ln + 2lnx) Solving 8ln + 8lnx = 1ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 8ln + -1ln + 8lnx = 1ln + -1ln + 2lnx Combine like terms: 8ln + -1ln = 7ln 7ln + 8lnx = 1ln + -1ln + 2lnx Combine like terms: 1ln + -1ln = 0 7ln + 8lnx = 0 + 2lnx 7ln + 8lnx = 2lnx Add '-2lnx' to each side of the equation. 7ln + 8lnx + -2lnx = 2lnx + -2lnx Combine like terms: 8lnx + -2lnx = 6lnx 7ln + 6lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 7ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + 6x) = 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 '(7 + 6x)' equal to zero and attempt to solve: Simplifying 7 + 6x = 0 Solving 7 + 6x = 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 + 6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x = 0 + -7 6x = 0 + -7 Combine like terms: 0 + -7 = -7 6x = -7 Add '-6x' to each side of the equation. 6x + -6x = -7 + -6x Combine like terms: 6x + -6x = 0 0 = -7 + -6x Simplifying 0 = -7 + -6x 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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