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Simplifying Log(8)(x + 3) + log(8)(x + 2) = log(8)(6) Reorder the terms: goL * 8(3 + x) + log(8)(x + 2) = log(8)(6) Reorder the terms for easier multiplication: 8goL(3 + x) + log(8)(x + 2) = log(8)(6) (3 * 8goL + x * 8goL) + log(8)(x + 2) = log(8)(6) (24goL + 8goxL) + log(8)(x + 2) = log(8)(6) Reorder the terms: 24goL + 8goxL + glo * 8(2 + x) = log(8)(6) Reorder the terms for easier multiplication: 24goL + 8goxL + 8glo(2 + x) = log(8)(6) 24goL + 8goxL + (2 * 8glo + x * 8glo) = log(8)(6) 24goL + 8goxL + (16glo + 8glox) = log(8)(6) Reorder the terms: 16glo + 8glox + 24goL + 8goxL = log(8)(6) Reorder the terms for easier multiplication: 16glo + 8glox + 24goL + 8goxL = 8 * 6glo Multiply 8 * 6 16glo + 8glox + 24goL + 8goxL = 48glo Solving 16glo + 8glox + 24goL + 8goxL = 48glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-48glo' to each side of the equation. 16glo + 8glox + 24goL + -48glo + 8goxL = 48glo + -48glo Reorder the terms: 16glo + -48glo + 8glox + 24goL + 8goxL = 48glo + -48glo Combine like terms: 16glo + -48glo = -32glo -32glo + 8glox + 24goL + 8goxL = 48glo + -48glo Combine like terms: 48glo + -48glo = 0 -32glo + 8glox + 24goL + 8goxL = 0 Factor out the Greatest Common Factor (GCF), '8go'. 8go(-4l + lx + 3L + xL) = 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 '(-4l + lx + 3L + xL)' equal to zero and attempt to solve: Simplifying -4l + lx + 3L + xL = 0 Reorder the terms: 3L + -4l + lx + xL = 0 Solving 3L + -4l + lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-3L' to each side of the equation. 3L + -4l + lx + -3L + xL = 0 + -3L Reorder the terms: 3L + -3L + -4l + lx + xL = 0 + -3L Combine like terms: 3L + -3L = 0 0 + -4l + lx + xL = 0 + -3L -4l + lx + xL = 0 + -3L Remove the zero: -4l + lx + xL = -3L Add '4l' to each side of the equation. -4l + lx + 4l + xL = -3L + 4l Reorder the terms: -4l + 4l + lx + xL = -3L + 4l Combine like terms: -4l + 4l = 0 0 + lx + xL = -3L + 4l lx + xL = -3L + 4l Add '-1lx' to each side of the equation. lx + -1lx + xL = -3L + 4l + -1lx Combine like terms: lx + -1lx = 0 0 + xL = -3L + 4l + -1lx xL = -3L + 4l + -1lx Add '-1xL' to each side of the equation. xL + -1xL = -3L + 4l + -1lx + -1xL Combine like terms: xL + -1xL = 0 0 = -3L + 4l + -1lx + -1xL Simplifying 0 = -3L + 4l + -1lx + -1xL 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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