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Simplifying Log(4x + -5) = Log(2x + 7) Reorder the terms: goL(-5 + 4x) = Log(2x + 7) (-5 * goL + 4x * goL) = Log(2x + 7) (-5goL + 4goxL) = Log(2x + 7) Reorder the terms: -5goL + 4goxL = goL(7 + 2x) -5goL + 4goxL = (7 * goL + 2x * goL) -5goL + 4goxL = (7goL + 2goxL) Solving -5goL + 4goxL = 7goL + 2goxL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7goL' to each side of the equation. -5goL + -7goL + 4goxL = 7goL + -7goL + 2goxL Combine like terms: -5goL + -7goL = -12goL -12goL + 4goxL = 7goL + -7goL + 2goxL Combine like terms: 7goL + -7goL = 0 -12goL + 4goxL = 0 + 2goxL -12goL + 4goxL = 2goxL Add '-2goxL' to each side of the equation. -12goL + 4goxL + -2goxL = 2goxL + -2goxL Combine like terms: 4goxL + -2goxL = 2goxL -12goL + 2goxL = 2goxL + -2goxL Combine like terms: 2goxL + -2goxL = 0 -12goL + 2goxL = 0 Factor out the Greatest Common Factor (GCF), '2goL'. 2goL(-6 + x) = 0 Ignore the factor 2.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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -1x 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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