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Simplifying Log[5](x) + log[5](x + 2) = log[5](8) Reorder the terms for easier multiplication: 5goL * x + log[5](x + 2) = log[5](8) Multiply goL * x 5goxL + log[5](x + 2) = log[5](8) Reorder the terms: 5goxL + glo * 5(2 + x) = log[5](8) Reorder the terms for easier multiplication: 5goxL + 5glo(2 + x) = log[5](8) 5goxL + (2 * 5glo + x * 5glo) = log[5](8) 5goxL + (10glo + 5glox) = log[5](8) Reorder the terms: 10glo + 5glox + 5goxL = log[5](8) Reorder the terms for easier multiplication: 10glo + 5glox + 5goxL = 5 * 8glo Multiply 5 * 8 10glo + 5glox + 5goxL = 40glo Solving 10glo + 5glox + 5goxL = 40glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-40glo' to each side of the equation. 10glo + 5glox + -40glo + 5goxL = 40glo + -40glo Reorder the terms: 10glo + -40glo + 5glox + 5goxL = 40glo + -40glo Combine like terms: 10glo + -40glo = -30glo -30glo + 5glox + 5goxL = 40glo + -40glo Combine like terms: 40glo + -40glo = 0 -30glo + 5glox + 5goxL = 0 Factor out the Greatest Common Factor (GCF), '5go'. 5go(-6l + lx + xL) = 0 Ignore the factor 5.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 '(-6l + lx + xL)' equal to zero and attempt to solve: Simplifying -6l + lx + xL = 0 Solving -6l + lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '6l' to each side of the equation. -6l + lx + 6l + xL = 0 + 6l Reorder the terms: -6l + 6l + lx + xL = 0 + 6l Combine like terms: -6l + 6l = 0 0 + lx + xL = 0 + 6l lx + xL = 0 + 6l Remove the zero: lx + xL = 6l Add '-1lx' to each side of the equation. lx + -1lx + xL = 6l + -1lx Combine like terms: lx + -1lx = 0 0 + xL = 6l + -1lx xL = 6l + -1lx Add '-1xL' to each side of the equation. xL + -1xL = 6l + -1lx + -1xL Combine like terms: xL + -1xL = 0 0 = 6l + -1lx + -1xL Simplifying 0 = 6l + -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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