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Simplifying log[5](x + 26) + log[5](x + 126) = 5 Reorder the terms: glo * 5(26 + x) + log[5](x + 126) = 5 Reorder the terms for easier multiplication: 5glo(26 + x) + log[5](x + 126) = 5 (26 * 5glo + x * 5glo) + log[5](x + 126) = 5 (130glo + 5glox) + log[5](x + 126) = 5 Reorder the terms: 130glo + 5glox + glo * 5(126 + x) = 5 Reorder the terms for easier multiplication: 130glo + 5glox + 5glo(126 + x) = 5 130glo + 5glox + (126 * 5glo + x * 5glo) = 5 130glo + 5glox + (630glo + 5glox) = 5 Reorder the terms: 130glo + 630glo + 5glox + 5glox = 5 Combine like terms: 130glo + 630glo = 760glo 760glo + 5glox + 5glox = 5 Combine like terms: 5glox + 5glox = 10glox 760glo + 10glox = 5 Solving 760glo + 10glox = 5 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -5 + 760glo + 10glox = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 760glo + 10glox = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + 152glo + 2glox) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + 152glo + 2glox)' equal to zero and attempt to solve: Simplifying -1 + 152glo + 2glox = 0 Solving -1 + 152glo + 2glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 152glo + 1 + 2glox = 0 + 1 Reorder the terms: -1 + 1 + 152glo + 2glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 152glo + 2glox = 0 + 1 152glo + 2glox = 0 + 1 Combine like terms: 0 + 1 = 1 152glo + 2glox = 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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