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Simplifying log(5)(10x + -1) = log(5)(9x + 7) Reorder the terms: glo * 5(-1 + 10x) = log(5)(9x + 7) Reorder the terms for easier multiplication: 5glo(-1 + 10x) = log(5)(9x + 7) (-1 * 5glo + 10x * 5glo) = log(5)(9x + 7) (-5glo + 50glox) = log(5)(9x + 7) Reorder the terms: -5glo + 50glox = glo * 5(7 + 9x) Reorder the terms for easier multiplication: -5glo + 50glox = 5glo(7 + 9x) -5glo + 50glox = (7 * 5glo + 9x * 5glo) -5glo + 50glox = (35glo + 45glox) Solving -5glo + 50glox = 35glo + 45glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-35glo' to each side of the equation. -5glo + -35glo + 50glox = 35glo + -35glo + 45glox Combine like terms: -5glo + -35glo = -40glo -40glo + 50glox = 35glo + -35glo + 45glox Combine like terms: 35glo + -35glo = 0 -40glo + 50glox = 0 + 45glox -40glo + 50glox = 45glox Add '-45glox' to each side of the equation. -40glo + 50glox + -45glox = 45glox + -45glox Combine like terms: 50glox + -45glox = 5glox -40glo + 5glox = 45glox + -45glox Combine like terms: 45glox + -45glox = 0 -40glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-8 + 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 '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Add '-1x' to each side of the equation. x + -1x = 8 + -1x Combine like terms: x + -1x = 0 0 = 8 + -1x Simplifying 0 = 8 + -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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