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Simplifying Log(8)(3x + 5) = log(8)(3x + 8) Reorder the terms: goL * 8(5 + 3x) = log(8)(3x + 8) Reorder the terms for easier multiplication: 8goL(5 + 3x) = log(8)(3x + 8) (5 * 8goL + 3x * 8goL) = log(8)(3x + 8) (40goL + 24goxL) = log(8)(3x + 8) Reorder the terms: 40goL + 24goxL = glo * 8(8 + 3x) Reorder the terms for easier multiplication: 40goL + 24goxL = 8glo(8 + 3x) 40goL + 24goxL = (8 * 8glo + 3x * 8glo) 40goL + 24goxL = (64glo + 24glox) Solving 40goL + 24goxL = 64glo + 24glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-64glo' to each side of the equation. 40goL + -64glo + 24goxL = 64glo + -64glo + 24glox Reorder the terms: -64glo + 40goL + 24goxL = 64glo + -64glo + 24glox Combine like terms: 64glo + -64glo = 0 -64glo + 40goL + 24goxL = 0 + 24glox -64glo + 40goL + 24goxL = 24glox Add '-24glox' to each side of the equation. -64glo + 40goL + -24glox + 24goxL = 24glox + -24glox Reorder the terms: -64glo + -24glox + 40goL + 24goxL = 24glox + -24glox Combine like terms: 24glox + -24glox = 0 -64glo + -24glox + 40goL + 24goxL = 0 Factor out the Greatest Common Factor (GCF), '8go'. 8go(-8l + -3lx + 5L + 3xL) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(-8l + -3lx + 5L + 3xL)' equal to zero and attempt to solve: Simplifying -8l + -3lx + 5L + 3xL = 0 Reorder the terms: 5L + -8l + -3lx + 3xL = 0 Solving 5L + -8l + -3lx + 3xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-5L' to each side of the equation. 5L + -8l + -3lx + -5L + 3xL = 0 + -5L Reorder the terms: 5L + -5L + -8l + -3lx + 3xL = 0 + -5L Combine like terms: 5L + -5L = 0 0 + -8l + -3lx + 3xL = 0 + -5L -8l + -3lx + 3xL = 0 + -5L Remove the zero: -8l + -3lx + 3xL = -5L Add '8l' to each side of the equation. -8l + -3lx + 8l + 3xL = -5L + 8l Reorder the terms: -8l + 8l + -3lx + 3xL = -5L + 8l Combine like terms: -8l + 8l = 0 0 + -3lx + 3xL = -5L + 8l -3lx + 3xL = -5L + 8l Add '3lx' to each side of the equation. -3lx + 3lx + 3xL = -5L + 8l + 3lx Combine like terms: -3lx + 3lx = 0 0 + 3xL = -5L + 8l + 3lx 3xL = -5L + 8l + 3lx Add '-3xL' to each side of the equation. 3xL + -3xL = -5L + 8l + 3lx + -3xL Combine like terms: 3xL + -3xL = 0 0 = -5L + 8l + 3lx + -3xL Simplifying 0 = -5L + 8l + 3lx + -3xL 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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