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Simplifying log[5](3x + 10) = log[5](2x + -6) Reorder the terms: glo * 5(10 + 3x) = log[5](2x + -6) Reorder the terms for easier multiplication: 5glo(10 + 3x) = log[5](2x + -6) (10 * 5glo + 3x * 5glo) = log[5](2x + -6) (50glo + 15glox) = log[5](2x + -6) Reorder the terms: 50glo + 15glox = glo * 5(-6 + 2x) Reorder the terms for easier multiplication: 50glo + 15glox = 5glo(-6 + 2x) 50glo + 15glox = (-6 * 5glo + 2x * 5glo) 50glo + 15glox = (-30glo + 10glox) Solving 50glo + 15glox = -30glo + 10glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '30glo' to each side of the equation. 50glo + 30glo + 15glox = -30glo + 30glo + 10glox Combine like terms: 50glo + 30glo = 80glo 80glo + 15glox = -30glo + 30glo + 10glox Combine like terms: -30glo + 30glo = 0 80glo + 15glox = 0 + 10glox 80glo + 15glox = 10glox Add '-10glox' to each side of the equation. 80glo + 15glox + -10glox = 10glox + -10glox Combine like terms: 15glox + -10glox = 5glox 80glo + 5glox = 10glox + -10glox Combine like terms: 10glox + -10glox = 0 80glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(16 + x) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(16 + x)' equal to zero and attempt to solve: Simplifying 16 + x = 0 Solving 16 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + x = 0 + -16 x = 0 + -16 Combine like terms: 0 + -16 = -16 x = -16 Add '-1x' to each side of the equation. x + -1x = -16 + -1x Combine like terms: x + -1x = 0 0 = -16 + -1x Simplifying 0 = -16 + -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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