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Simplifying log[5](5y + 40) + -1log[5](y + 2) = 2 Reorder the terms: glo * 5(40 + 5y) + -1log[5](y + 2) = 2 Reorder the terms for easier multiplication: 5glo(40 + 5y) + -1log[5](y + 2) = 2 (40 * 5glo + 5y * 5glo) + -1log[5](y + 2) = 2 (200glo + 25gloy) + -1log[5](y + 2) = 2 Reorder the terms: 200glo + 25gloy + -1glo * 5(2 + y) = 2 Reorder the terms for easier multiplication: 200glo + 25gloy + -1 * 5glo(2 + y) = 2 Multiply -1 * 5 200glo + 25gloy + -5glo(2 + y) = 2 200glo + 25gloy + (2 * -5glo + y * -5glo) = 2 200glo + 25gloy + (-10glo + -5gloy) = 2 Reorder the terms: 200glo + -10glo + 25gloy + -5gloy = 2 Combine like terms: 200glo + -10glo = 190glo 190glo + 25gloy + -5gloy = 2 Combine like terms: 25gloy + -5gloy = 20gloy 190glo + 20gloy = 2 Solving 190glo + 20gloy = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + 190glo + 20gloy = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 190glo + 20gloy = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 95glo + 10gloy) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 95glo + 10gloy)' equal to zero and attempt to solve: Simplifying -1 + 95glo + 10gloy = 0 Solving -1 + 95glo + 10gloy = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 95glo + 1 + 10gloy = 0 + 1 Reorder the terms: -1 + 1 + 95glo + 10gloy = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 95glo + 10gloy = 0 + 1 95glo + 10gloy = 0 + 1 Combine like terms: 0 + 1 = 1 95glo + 10gloy = 1 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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