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Simplifying log(x + -5) = log(150) + -1log(x) Reorder the terms: glo(-5 + x) = log(150) + -1log(x) (-5 * glo + x * glo) = log(150) + -1log(x) (-5glo + glox) = log(150) + -1log(x) Reorder the terms for easier multiplication: -5glo + glox = 150glo + -1log(x) Multiply glo * x -5glo + glox = 150glo + -1glox Solving -5glo + glox = 150glo + -1glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-150glo' to each side of the equation. -5glo + -150glo + glox = 150glo + -150glo + -1glox Combine like terms: -5glo + -150glo = -155glo -155glo + glox = 150glo + -150glo + -1glox Combine like terms: 150glo + -150glo = 0 -155glo + glox = 0 + -1glox -155glo + glox = -1glox Add 'glox' to each side of the equation. -155glo + glox + glox = -1glox + glox Combine like terms: glox + glox = 2glox -155glo + 2glox = -1glox + glox Combine like terms: -1glox + glox = 0 -155glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-155 + 2x) = 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 '(-155 + 2x)' equal to zero and attempt to solve: Simplifying -155 + 2x = 0 Solving -155 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '155' to each side of the equation. -155 + 155 + 2x = 0 + 155 Combine like terms: -155 + 155 = 0 0 + 2x = 0 + 155 2x = 0 + 155 Combine like terms: 0 + 155 = 155 2x = 155 Add '-2x' to each side of the equation. 2x + -2x = 155 + -2x Combine like terms: 2x + -2x = 0 0 = 155 + -2x Simplifying 0 = 155 + -2x 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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