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Simplifying log(7)(8x + 5) = log(7)(6x + -18) Reorder the terms: glo * 7(5 + 8x) = log(7)(6x + -18) Reorder the terms for easier multiplication: 7glo(5 + 8x) = log(7)(6x + -18) (5 * 7glo + 8x * 7glo) = log(7)(6x + -18) (35glo + 56glox) = log(7)(6x + -18) Reorder the terms: 35glo + 56glox = glo * 7(-18 + 6x) Reorder the terms for easier multiplication: 35glo + 56glox = 7glo(-18 + 6x) 35glo + 56glox = (-18 * 7glo + 6x * 7glo) 35glo + 56glox = (-126glo + 42glox) Solving 35glo + 56glox = -126glo + 42glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '126glo' to each side of the equation. 35glo + 126glo + 56glox = -126glo + 126glo + 42glox Combine like terms: 35glo + 126glo = 161glo 161glo + 56glox = -126glo + 126glo + 42glox Combine like terms: -126glo + 126glo = 0 161glo + 56glox = 0 + 42glox 161glo + 56glox = 42glox Add '-42glox' to each side of the equation. 161glo + 56glox + -42glox = 42glox + -42glox Combine like terms: 56glox + -42glox = 14glox 161glo + 14glox = 42glox + -42glox Combine like terms: 42glox + -42glox = 0 161glo + 14glox = 0 Factor out the Greatest Common Factor (GCF), '7glo'. 7glo(23 + 2x) = 0 Ignore the factor 7.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 '(23 + 2x)' equal to zero and attempt to solve: Simplifying 23 + 2x = 0 Solving 23 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 2x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 2x = 0 + -23 2x = 0 + -23 Combine like terms: 0 + -23 = -23 2x = -23 Add '-2x' to each side of the equation. 2x + -2x = -23 + -2x Combine like terms: 2x + -2x = 0 0 = -23 + -2x Simplifying 0 = -23 + -2x 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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