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Simplifying log[5](x + 22) = 2 + -1log[5](x + -2) Reorder the terms: glo * 5(22 + x) = 2 + -1log[5](x + -2) Reorder the terms for easier multiplication: 5glo(22 + x) = 2 + -1log[5](x + -2) (22 * 5glo + x * 5glo) = 2 + -1log[5](x + -2) (110glo + 5glox) = 2 + -1log[5](x + -2) Reorder the terms: 110glo + 5glox = 2 + -1glo * 5(-2 + x) Reorder the terms for easier multiplication: 110glo + 5glox = 2 + -1 * 5glo(-2 + x) Multiply -1 * 5 110glo + 5glox = 2 + -5glo(-2 + x) 110glo + 5glox = 2 + (-2 * -5glo + x * -5glo) 110glo + 5glox = 2 + (10glo + -5glox) Solving 110glo + 5glox = 2 + 10glo + -5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10glo' to each side of the equation. 110glo + -10glo + 5glox = 2 + 10glo + -10glo + -5glox Combine like terms: 110glo + -10glo = 100glo 100glo + 5glox = 2 + 10glo + -10glo + -5glox Combine like terms: 10glo + -10glo = 0 100glo + 5glox = 2 + 0 + -5glox 100glo + 5glox = 2 + -5glox Add '5glox' to each side of the equation. 100glo + 5glox + 5glox = 2 + -5glox + 5glox Combine like terms: 5glox + 5glox = 10glox 100glo + 10glox = 2 + -5glox + 5glox Combine like terms: -5glox + 5glox = 0 100glo + 10glox = 2 + 0 100glo + 10glox = 2 Reorder the terms: -2 + 100glo + 10glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 100glo + 10glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 50glo + 5glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 50glo + 5glox)' equal to zero and attempt to solve: Simplifying -1 + 50glo + 5glox = 0 Solving -1 + 50glo + 5glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 50glo + 1 + 5glox = 0 + 1 Reorder the terms: -1 + 1 + 50glo + 5glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 50glo + 5glox = 0 + 1 50glo + 5glox = 0 + 1 Combine like terms: 0 + 1 = 1 50glo + 5glox = 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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