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Simplifying log(x + 6) + -2 = 0.5log(3x + -3) + -1log(25) Reorder the terms: glo(6 + x) + -2 = 0.5log(3x + -3) + -1log(25) (6 * glo + x * glo) + -2 = 0.5log(3x + -3) + -1log(25) (6glo + glox) + -2 = 0.5log(3x + -3) + -1log(25) Reorder the terms: -2 + 6glo + glox = 0.5log(3x + -3) + -1log(25) Reorder the terms: -2 + 6glo + glox = 0.5glo(-3 + 3x) + -1log(25) -2 + 6glo + glox = (-3 * 0.5glo + 3x * 0.5glo) + -1log(25) -2 + 6glo + glox = (-1.5glo + 1.5glox) + -1log(25) Reorder the terms for easier multiplication: -2 + 6glo + glox = -1.5glo + 1.5glox + -1 * 25glo Multiply -1 * 25 -2 + 6glo + glox = -1.5glo + 1.5glox + -25glo Reorder the terms: -2 + 6glo + glox = -1.5glo + -25glo + 1.5glox Combine like terms: -1.5glo + -25glo = -26.5glo -2 + 6glo + glox = -26.5glo + 1.5glox Solving -2 + 6glo + glox = -26.5glo + 1.5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '26.5glo' to each side of the equation. -2 + 6glo + 26.5glo + glox = -26.5glo + 26.5glo + 1.5glox Combine like terms: 6glo + 26.5glo = 32.5glo -2 + 32.5glo + glox = -26.5glo + 26.5glo + 1.5glox Combine like terms: -26.5glo + 26.5glo = 0.0 -2 + 32.5glo + glox = 0.0 + 1.5glox -2 + 32.5glo + glox = 1.5glox Add '-1.5glox' to each side of the equation. -2 + 32.5glo + glox + -1.5glox = 1.5glox + -1.5glox Combine like terms: glox + -1.5glox = -0.5glox -2 + 32.5glo + -0.5glox = 1.5glox + -1.5glox Combine like terms: 1.5glox + -1.5glox = 0.0 -2 + 32.5glo + -0.5glox = 0.0 Add '2' to each side of the equation. -2 + 32.5glo + 2 + -0.5glox = 0.0 + 2 Reorder the terms: -2 + 2 + 32.5glo + -0.5glox = 0.0 + 2 Combine like terms: -2 + 2 = 0 0 + 32.5glo + -0.5glox = 0.0 + 2 32.5glo + -0.5glox = 0.0 + 2 Combine like terms: 0.0 + 2 = 2 32.5glo + -0.5glox = 2 Reorder the terms: -2 + 32.5glo + -0.5glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 32.5glo + -0.5glox = 0 The solution to this equation could not be determined.
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