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Simplifying in(x + 1) + ln(x + 3) = ln(x + 7) Reorder the terms: in(1 + x) + ln(x + 3) = ln(x + 7) (1 * in + x * in) + ln(x + 3) = ln(x + 7) (1in + inx) + ln(x + 3) = ln(x + 7) Reorder the terms: 1in + inx + ln(3 + x) = ln(x + 7) 1in + inx + (3 * ln + x * ln) = ln(x + 7) 1in + inx + (3ln + lnx) = ln(x + 7) Reorder the terms: 1in + inx + 3ln + lnx = ln(7 + x) 1in + inx + 3ln + lnx = (7 * ln + x * ln) 1in + inx + 3ln + lnx = (7ln + lnx) Add '-1lnx' to each side of the equation. 1in + inx + 3ln + lnx + -1lnx = 7ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 1in + inx + 3ln + 0 = 7ln + lnx + -1lnx 1in + inx + 3ln = 7ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 1in + inx + 3ln = 7ln + 0 1in + inx + 3ln = 7ln Solving 1in + inx + 3ln = 7ln Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3ln' to each side of the equation. 1in + inx + 3ln + -3ln = 7ln + -3ln Combine like terms: 3ln + -3ln = 0 1in + inx + 0 = 7ln + -3ln 1in + inx = 7ln + -3ln Combine like terms: 7ln + -3ln = 4ln 1in + inx = 4ln Combine like terms: 4ln + -4ln = 0 1in + inx + -4ln = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(i + ix + -4l) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing i to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(i + ix + -4l)' equal to zero and attempt to solve: Simplifying i + ix + -4l = 0 Solving i + ix + -4l = 0 Move all terms containing i to the left, all other terms to the right. Add '4l' to each side of the equation. i + ix + -4l + 4l = 0 + 4l Combine like terms: -4l + 4l = 0 i + ix + 0 = 0 + 4l i + ix = 0 + 4l Remove the zero: i + ix = 4l 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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