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Simplifying Log(x) + Log(x + -11) = Log(4x) Multiply goL * x goxL + Log(x + -11) = Log(4x) Reorder the terms: goxL + goL(-11 + x) = Log(4x) goxL + (-11 * goL + x * goL) = Log(4x) goxL + (-11goL + goxL) = Log(4x) Reorder the terms: -11goL + goxL + goxL = Log(4x) Combine like terms: goxL + goxL = 2goxL -11goL + 2goxL = Log(4x) Remove parenthesis around (4x) -11goL + 2goxL = goL * 4x Reorder the terms for easier multiplication: -11goL + 2goxL = 4goL * x Multiply goL * x -11goL + 2goxL = 4goxL Solving -11goL + 2goxL = 4goxL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4goxL' to each side of the equation. -11goL + 2goxL + -4goxL = 4goxL + -4goxL Combine like terms: 2goxL + -4goxL = -2goxL -11goL + -2goxL = 4goxL + -4goxL Combine like terms: 4goxL + -4goxL = 0 -11goL + -2goxL = 0 Factor out the Greatest Common Factor (GCF), '-1goL'. -1goL(11 + 2x) = 0 Ignore the factor -1.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 '(11 + 2x)' equal to zero and attempt to solve: Simplifying 11 + 2x = 0 Solving 11 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 2x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 2x = 0 + -11 2x = 0 + -11 Combine like terms: 0 + -11 = -11 2x = -11 Add '-2x' to each side of the equation. 2x + -2x = -11 + -2x Combine like terms: 2x + -2x = 0 0 = -11 + -2x Simplifying 0 = -11 + -2x 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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