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Simplifying log[5](x + 2) = log[5](9x + -5) Reorder the terms: glo * 5(2 + x) = log[5](9x + -5) Reorder the terms for easier multiplication: 5glo(2 + x) = log[5](9x + -5) (2 * 5glo + x * 5glo) = log[5](9x + -5) (10glo + 5glox) = log[5](9x + -5) Reorder the terms: 10glo + 5glox = glo * 5(-5 + 9x) Reorder the terms for easier multiplication: 10glo + 5glox = 5glo(-5 + 9x) 10glo + 5glox = (-5 * 5glo + 9x * 5glo) 10glo + 5glox = (-25glo + 45glox) Solving 10glo + 5glox = -25glo + 45glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '25glo' to each side of the equation. 10glo + 25glo + 5glox = -25glo + 25glo + 45glox Combine like terms: 10glo + 25glo = 35glo 35glo + 5glox = -25glo + 25glo + 45glox Combine like terms: -25glo + 25glo = 0 35glo + 5glox = 0 + 45glox 35glo + 5glox = 45glox Add '-45glox' to each side of the equation. 35glo + 5glox + -45glox = 45glox + -45glox Combine like terms: 5glox + -45glox = -40glox 35glo + -40glox = 45glox + -45glox Combine like terms: 45glox + -45glox = 0 35glo + -40glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(7 + -8x) = 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 '(7 + -8x)' equal to zero and attempt to solve: Simplifying 7 + -8x = 0 Solving 7 + -8x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -8x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8x = 0 + -7 -8x = 0 + -7 Combine like terms: 0 + -7 = -7 -8x = -7 Add '8x' to each side of the equation. -8x + 8x = -7 + 8x Combine like terms: -8x + 8x = 0 0 = -7 + 8x Simplifying 0 = -7 + 8x 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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