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Simplifying Log[9](3 + -1x) = Log[9](5x + -15) Reorder the terms for easier multiplication: 9goL(3 + -1x) = Log[9](5x + -15) (3 * 9goL + -1x * 9goL) = Log[9](5x + -15) (27goL + -9goxL) = Log[9](5x + -15) Reorder the terms: 27goL + -9goxL = goL * 9(-15 + 5x) Reorder the terms for easier multiplication: 27goL + -9goxL = 9goL(-15 + 5x) 27goL + -9goxL = (-15 * 9goL + 5x * 9goL) 27goL + -9goxL = (-135goL + 45goxL) Solving 27goL + -9goxL = -135goL + 45goxL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '135goL' to each side of the equation. 27goL + 135goL + -9goxL = -135goL + 135goL + 45goxL Combine like terms: 27goL + 135goL = 162goL 162goL + -9goxL = -135goL + 135goL + 45goxL Combine like terms: -135goL + 135goL = 0 162goL + -9goxL = 0 + 45goxL 162goL + -9goxL = 45goxL Add '-45goxL' to each side of the equation. 162goL + -9goxL + -45goxL = 45goxL + -45goxL Combine like terms: -9goxL + -45goxL = -54goxL 162goL + -54goxL = 45goxL + -45goxL Combine like terms: 45goxL + -45goxL = 0 162goL + -54goxL = 0 Factor out the Greatest Common Factor (GCF), '54goL'. 54goL(3 + -1x) = 0 Ignore the factor 54.Subproblem 1
Set the factor 'goL' equal to zero and attempt to solve: Simplifying goL = 0 Solving goL = 0 Move all terms containing g to the left, all other terms to the right. Simplifying goL = 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 g 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. The solution to this equation could not be determined.
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