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Simplifying ln(7x + 9) + ln(5x) = ln(x2) Reorder the terms: ln(9 + 7x) + ln(5x) = ln(x2) (9 * ln + 7x * ln) + ln(5x) = ln(x2) (9ln + 7lnx) + ln(5x) = ln(x2) Remove parenthesis around (5x) 9ln + 7lnx + ln * 5x = ln(x2) Reorder the terms for easier multiplication: 9ln + 7lnx + 5ln * x = ln(x2) Multiply ln * x 9ln + 7lnx + 5lnx = ln(x2) Combine like terms: 7lnx + 5lnx = 12lnx 9ln + 12lnx = ln(x2) Multiply ln * x2 9ln + 12lnx = lnx2 Solving 9ln + 12lnx = lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx2' to each side of the equation. 9ln + 12lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 9ln + 12lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + 12x + -1x2) = 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 '(9 + 12x + -1x2)' equal to zero and attempt to solve: Simplifying 9 + 12x + -1x2 = 0 Solving 9 + 12x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + 12x + -9 + -1x2 = 0 + -9 Reorder the terms: 9 + -9 + 12x + -1x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 12x + -1x2 = 0 + -9 12x + -1x2 = 0 + -9 Combine like terms: 0 + -9 = -9 12x + -1x2 = -9 Add '-12x' to each side of the equation. 12x + -12x + -1x2 = -9 + -12x Combine like terms: 12x + -12x = 0 0 + -1x2 = -9 + -12x -1x2 = -9 + -12x Add 'x2' to each side of the equation. -1x2 + x2 = -9 + -12x + x2 Combine like terms: -1x2 + x2 = 0 0 = -9 + -12x + x2 Simplifying 0 = -9 + -12x + x2 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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