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Simplifying long[5](x + -1) + -1log[5](x + 4) = log[5](x + -5) Reorder the terms: glno * 5(-1 + x) + -1log[5](x + 4) = log[5](x + -5) Reorder the terms for easier multiplication: 5glno(-1 + x) + -1log[5](x + 4) = log[5](x + -5) (-1 * 5glno + x * 5glno) + -1log[5](x + 4) = log[5](x + -5) (-5glno + 5glnox) + -1log[5](x + 4) = log[5](x + -5) Reorder the terms: -5glno + 5glnox + -1glo * 5(4 + x) = log[5](x + -5) Reorder the terms for easier multiplication: -5glno + 5glnox + -1 * 5glo(4 + x) = log[5](x + -5) Multiply -1 * 5 -5glno + 5glnox + -5glo(4 + x) = log[5](x + -5) -5glno + 5glnox + (4 * -5glo + x * -5glo) = log[5](x + -5) -5glno + 5glnox + (-20glo + -5glox) = log[5](x + -5) Reorder the terms: -5glno + 5glnox + -20glo + -5glox = glo * 5(-5 + x) Reorder the terms for easier multiplication: -5glno + 5glnox + -20glo + -5glox = 5glo(-5 + x) -5glno + 5glnox + -20glo + -5glox = (-5 * 5glo + x * 5glo) -5glno + 5glnox + -20glo + -5glox = (-25glo + 5glox) Solving -5glno + 5glnox + -20glo + -5glox = -25glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '25glo' to each side of the equation. -5glno + 5glnox + -20glo + 25glo + -5glox = -25glo + 25glo + 5glox Combine like terms: -20glo + 25glo = 5glo -5glno + 5glnox + 5glo + -5glox = -25glo + 25glo + 5glox Combine like terms: -25glo + 25glo = 0 -5glno + 5glnox + 5glo + -5glox = 0 + 5glox -5glno + 5glnox + 5glo + -5glox = 5glox Add '-5glox' to each side of the equation. -5glno + 5glnox + 5glo + -5glox + -5glox = 5glox + -5glox Combine like terms: -5glox + -5glox = -10glox -5glno + 5glnox + 5glo + -10glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -5glno + 5glnox + 5glo + -10glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-1n + nx + 1 + -2x) = 0 Ignore the factor 5.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 '(-1n + nx + 1 + -2x)' equal to zero and attempt to solve: Simplifying -1n + nx + 1 + -2x = 0 Reorder the terms: 1 + -1n + nx + -2x = 0 Solving 1 + -1n + nx + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1n + nx + -1 + -2x = 0 + -1 Reorder the terms: 1 + -1 + -1n + nx + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n + nx + -2x = 0 + -1 -1n + nx + -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -1n + nx + -2x = -1 Add 'n' to each side of the equation. -1n + nx + n + -2x = -1 + n Reorder the terms: -1n + n + nx + -2x = -1 + n Combine like terms: -1n + n = 0 0 + nx + -2x = -1 + n nx + -2x = -1 + n Add '-1nx' to each side of the equation. nx + -1nx + -2x = -1 + n + -1nx Combine like terms: nx + -1nx = 0 0 + -2x = -1 + n + -1nx -2x = -1 + n + -1nx Add '2x' to each side of the equation. -2x + 2x = -1 + n + -1nx + 2x Combine like terms: -2x + 2x = 0 0 = -1 + n + -1nx + 2x Simplifying 0 = -1 + n + -1nx + 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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