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Simplifying lg(x + 42) + -2lgx = 0 Reorder the terms: gl(42 + x) + -2lgx = 0 (42 * gl + x * gl) + -2lgx = 0 (42gl + glx) + -2lgx = 0 Combine like terms: glx + -2glx = -1glx 42gl + -1glx = 0 Solving 42gl + -1glx = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'gl'. gl(42 + -1x) = 0Subproblem 1
Set the factor 'gl' equal to zero and attempt to solve: Simplifying gl = 0 Solving gl = 0 Move all terms containing g to the left, all other terms to the right. Simplifying gl = 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 '(42 + -1x)' equal to zero and attempt to solve: Simplifying 42 + -1x = 0 Solving 42 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + -1x = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -1x = 0 + -42 -1x = 0 + -42 Combine like terms: 0 + -42 = -42 -1x = -42 Add 'x' to each side of the equation. -1x + x = -42 + x Combine like terms: -1x + x = 0 0 = -42 + x Simplifying 0 = -42 + x 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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