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Simplifying log(7)[x + -5] = log(7)[6x] Reorder the terms: glo * 7[-5 + x] = log(7)[6x] Reorder the terms for easier multiplication: 7glo[-5 + x] = log(7)[6x] [-5 * 7glo + x * 7glo] = log(7)[6x] [-35glo + 7glox] = log(7)[6x] Remove brackets around [6x] -35glo + 7glox = glo * 7 * 6x Reorder the terms for easier multiplication: -35glo + 7glox = 7 * 6glo * x Multiply 7 * 6 -35glo + 7glox = 42glo * x Multiply glo * x -35glo + 7glox = 42glox Solving -35glo + 7glox = 42glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-42glox' to each side of the equation. -35glo + 7glox + -42glox = 42glox + -42glox Combine like terms: 7glox + -42glox = -35glox -35glo + -35glox = 42glox + -42glox Combine like terms: 42glox + -42glox = 0 -35glo + -35glox = 0 Factor out the Greatest Common Factor (GCF), '-35glo'. -35glo(1 + x) = 0 Ignore the factor -35.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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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