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Simplifying log(5)[2x + 15] = log(5)[6x + -25] Reorder the terms: glo * 5[15 + 2x] = log(5)[6x + -25] Reorder the terms for easier multiplication: 5glo[15 + 2x] = log(5)[6x + -25] [15 * 5glo + 2x * 5glo] = log(5)[6x + -25] [75glo + 10glox] = log(5)[6x + -25] Reorder the terms: 75glo + 10glox = glo * 5[-25 + 6x] Reorder the terms for easier multiplication: 75glo + 10glox = 5glo[-25 + 6x] 75glo + 10glox = [-25 * 5glo + 6x * 5glo] 75glo + 10glox = [-125glo + 30glox] Solving 75glo + 10glox = -125glo + 30glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '125glo' to each side of the equation. 75glo + 125glo + 10glox = -125glo + 125glo + 30glox Combine like terms: 75glo + 125glo = 200glo 200glo + 10glox = -125glo + 125glo + 30glox Combine like terms: -125glo + 125glo = 0 200glo + 10glox = 0 + 30glox 200glo + 10glox = 30glox Add '-30glox' to each side of the equation. 200glo + 10glox + -30glox = 30glox + -30glox Combine like terms: 10glox + -30glox = -20glox 200glo + -20glox = 30glox + -30glox Combine like terms: 30glox + -30glox = 0 200glo + -20glox = 0 Factor out the Greatest Common Factor (GCF), '20glo'. 20glo(10 + -1x) = 0 Ignore the factor 20.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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Add 'x' to each side of the equation. -1x + x = -10 + x Combine like terms: -1x + x = 0 0 = -10 + x Simplifying 0 = -10 + 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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