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Simplifying log(8)(x + 6) = log(8)(4x + -9) Reorder the terms: glo * 8(6 + x) = log(8)(4x + -9) Reorder the terms for easier multiplication: 8glo(6 + x) = log(8)(4x + -9) (6 * 8glo + x * 8glo) = log(8)(4x + -9) (48glo + 8glox) = log(8)(4x + -9) Reorder the terms: 48glo + 8glox = glo * 8(-9 + 4x) Reorder the terms for easier multiplication: 48glo + 8glox = 8glo(-9 + 4x) 48glo + 8glox = (-9 * 8glo + 4x * 8glo) 48glo + 8glox = (-72glo + 32glox) Solving 48glo + 8glox = -72glo + 32glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '72glo' to each side of the equation. 48glo + 72glo + 8glox = -72glo + 72glo + 32glox Combine like terms: 48glo + 72glo = 120glo 120glo + 8glox = -72glo + 72glo + 32glox Combine like terms: -72glo + 72glo = 0 120glo + 8glox = 0 + 32glox 120glo + 8glox = 32glox Add '-32glox' to each side of the equation. 120glo + 8glox + -32glox = 32glox + -32glox Combine like terms: 8glox + -32glox = -24glox 120glo + -24glox = 32glox + -32glox Combine like terms: 32glox + -32glox = 0 120glo + -24glox = 0 Factor out the Greatest Common Factor (GCF), '24glo'. 24glo(5 + -1x) = 0 Ignore the factor 24.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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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