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Simplifying log(5)[x + -5] = log(7)[6x] Reorder the terms: glo * 5[-5 + x] = log(7)[6x] Reorder the terms for easier multiplication: 5glo[-5 + x] = log(7)[6x] [-5 * 5glo + x * 5glo] = log(7)[6x] [-25glo + 5glox] = log(7)[6x] Remove brackets around [6x] -25glo + 5glox = glo * 7 * 6x Reorder the terms for easier multiplication: -25glo + 5glox = 7 * 6glo * x Multiply 7 * 6 -25glo + 5glox = 42glo * x Multiply glo * x -25glo + 5glox = 42glox Solving -25glo + 5glox = 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. -25glo + 5glox + -42glox = 42glox + -42glox Combine like terms: 5glox + -42glox = -37glox -25glo + -37glox = 42glox + -42glox Combine like terms: 42glox + -42glox = 0 -25glo + -37glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(25 + 37x) = 0 Ignore the factor -1.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 '(25 + 37x)' equal to zero and attempt to solve: Simplifying 25 + 37x = 0 Solving 25 + 37x = 0 Move all terms containing g to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 37x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 37x = 0 + -25 37x = 0 + -25 Combine like terms: 0 + -25 = -25 37x = -25 Add '-37x' to each side of the equation. 37x + -37x = -25 + -37x Combine like terms: 37x + -37x = 0 0 = -25 + -37x Simplifying 0 = -25 + -37x 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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