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Simplifying Log(5x + 2) = Log(2x + 5) Reorder the terms: goL(2 + 5x) = Log(2x + 5) (2 * goL + 5x * goL) = Log(2x + 5) (2goL + 5goxL) = Log(2x + 5) Reorder the terms: 2goL + 5goxL = goL(5 + 2x) 2goL + 5goxL = (5 * goL + 2x * goL) 2goL + 5goxL = (5goL + 2goxL) Solving 2goL + 5goxL = 5goL + 2goxL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5goL' to each side of the equation. 2goL + -5goL + 5goxL = 5goL + -5goL + 2goxL Combine like terms: 2goL + -5goL = -3goL -3goL + 5goxL = 5goL + -5goL + 2goxL Combine like terms: 5goL + -5goL = 0 -3goL + 5goxL = 0 + 2goxL -3goL + 5goxL = 2goxL Add '-2goxL' to each side of the equation. -3goL + 5goxL + -2goxL = 2goxL + -2goxL Combine like terms: 5goxL + -2goxL = 3goxL -3goL + 3goxL = 2goxL + -2goxL Combine like terms: 2goxL + -2goxL = 0 -3goL + 3goxL = 0 Factor out the Greatest Common Factor (GCF), '3goL'. 3goL(-1 + x) = 0 Ignore the factor 3.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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