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Simplifying log(5)(5x + -7) = log(18)(x + -9) Reorder the terms: glo * 5(-7 + 5x) = log(18)(x + -9) Reorder the terms for easier multiplication: 5glo(-7 + 5x) = log(18)(x + -9) (-7 * 5glo + 5x * 5glo) = log(18)(x + -9) (-35glo + 25glox) = log(18)(x + -9) Reorder the terms: -35glo + 25glox = glo * 18(-9 + x) Reorder the terms for easier multiplication: -35glo + 25glox = 18glo(-9 + x) -35glo + 25glox = (-9 * 18glo + x * 18glo) -35glo + 25glox = (-162glo + 18glox) Solving -35glo + 25glox = -162glo + 18glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '162glo' to each side of the equation. -35glo + 162glo + 25glox = -162glo + 162glo + 18glox Combine like terms: -35glo + 162glo = 127glo 127glo + 25glox = -162glo + 162glo + 18glox Combine like terms: -162glo + 162glo = 0 127glo + 25glox = 0 + 18glox 127glo + 25glox = 18glox Add '-18glox' to each side of the equation. 127glo + 25glox + -18glox = 18glox + -18glox Combine like terms: 25glox + -18glox = 7glox 127glo + 7glox = 18glox + -18glox Combine like terms: 18glox + -18glox = 0 127glo + 7glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(127 + 7x) = 0Subproblem 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 '(127 + 7x)' equal to zero and attempt to solve: Simplifying 127 + 7x = 0 Solving 127 + 7x = 0 Move all terms containing g to the left, all other terms to the right. Add '-127' to each side of the equation. 127 + -127 + 7x = 0 + -127 Combine like terms: 127 + -127 = 0 0 + 7x = 0 + -127 7x = 0 + -127 Combine like terms: 0 + -127 = -127 7x = -127 Add '-7x' to each side of the equation. 7x + -7x = -127 + -7x Combine like terms: 7x + -7x = 0 0 = -127 + -7x Simplifying 0 = -127 + -7x 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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