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Simplifying log(8x + -5) = log(4x + 19) Reorder the terms: glo(-5 + 8x) = log(4x + 19) (-5 * glo + 8x * glo) = log(4x + 19) (-5glo + 8glox) = log(4x + 19) Reorder the terms: -5glo + 8glox = glo(19 + 4x) -5glo + 8glox = (19 * glo + 4x * glo) -5glo + 8glox = (19glo + 4glox) Solving -5glo + 8glox = 19glo + 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-19glo' to each side of the equation. -5glo + -19glo + 8glox = 19glo + -19glo + 4glox Combine like terms: -5glo + -19glo = -24glo -24glo + 8glox = 19glo + -19glo + 4glox Combine like terms: 19glo + -19glo = 0 -24glo + 8glox = 0 + 4glox -24glo + 8glox = 4glox Add '-4glox' to each side of the equation. -24glo + 8glox + -4glox = 4glox + -4glox Combine like terms: 8glox + -4glox = 4glox -24glo + 4glox = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -24glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(-6 + x) = 0 Ignore the factor 4.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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -1x 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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