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Simplifying log[8](x) + log[8](x + 3) = log[8](x + 48) Reorder the terms for easier multiplication: 8glo * x + log[8](x + 3) = log[8](x + 48) Multiply glo * x 8glox + log[8](x + 3) = log[8](x + 48) Reorder the terms: 8glox + glo * 8(3 + x) = log[8](x + 48) Reorder the terms for easier multiplication: 8glox + 8glo(3 + x) = log[8](x + 48) 8glox + (3 * 8glo + x * 8glo) = log[8](x + 48) 8glox + (24glo + 8glox) = log[8](x + 48) Reorder the terms: 24glo + 8glox + 8glox = log[8](x + 48) Combine like terms: 8glox + 8glox = 16glox 24glo + 16glox = log[8](x + 48) Reorder the terms: 24glo + 16glox = glo * 8(48 + x) Reorder the terms for easier multiplication: 24glo + 16glox = 8glo(48 + x) 24glo + 16glox = (48 * 8glo + x * 8glo) 24glo + 16glox = (384glo + 8glox) Solving 24glo + 16glox = 384glo + 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-384glo' to each side of the equation. 24glo + -384glo + 16glox = 384glo + -384glo + 8glox Combine like terms: 24glo + -384glo = -360glo -360glo + 16glox = 384glo + -384glo + 8glox Combine like terms: 384glo + -384glo = 0 -360glo + 16glox = 0 + 8glox -360glo + 16glox = 8glox Add '-8glox' to each side of the equation. -360glo + 16glox + -8glox = 8glox + -8glox Combine like terms: 16glox + -8glox = 8glox -360glo + 8glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 -360glo + 8glox = 0 Factor out the Greatest Common Factor (GCF), '8glo'. 8glo(-45 + x) = 0 Ignore the factor 8.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 '(-45 + x)' equal to zero and attempt to solve: Simplifying -45 + x = 0 Solving -45 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 0 + 45 Combine like terms: -45 + 45 = 0 0 + x = 0 + 45 x = 0 + 45 Combine like terms: 0 + 45 = 45 x = 45 Add '-1x' to each side of the equation. x + -1x = 45 + -1x Combine like terms: x + -1x = 0 0 = 45 + -1x Simplifying 0 = 45 + -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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