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Simplifying log(5)[5x + 9] = log(6x) Reorder the terms: glo * 5[9 + 5x] = log(6x) Reorder the terms for easier multiplication: 5glo[9 + 5x] = log(6x) [9 * 5glo + 5x * 5glo] = log(6x) [45glo + 25glox] = log(6x) Remove parenthesis around (6x) 45glo + 25glox = glo * 6x Reorder the terms for easier multiplication: 45glo + 25glox = 6glo * x Multiply glo * x 45glo + 25glox = 6glox Solving 45glo + 25glox = 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glox' to each side of the equation. 45glo + 25glox + -6glox = 6glox + -6glox Combine like terms: 25glox + -6glox = 19glox 45glo + 19glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 45glo + 19glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(45 + 19x) = 0Subproblem 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 '(45 + 19x)' equal to zero and attempt to solve: Simplifying 45 + 19x = 0 Solving 45 + 19x = 0 Move all terms containing g to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + 19x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 19x = 0 + -45 19x = 0 + -45 Combine like terms: 0 + -45 = -45 19x = -45 Add '-19x' to each side of the equation. 19x + -19x = -45 + -19x Combine like terms: 19x + -19x = 0 0 = -45 + -19x Simplifying 0 = -45 + -19x 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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