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Simplifying log(4)(5x + -3) + -1log(4)(9 + -1x) = 3 Reorder the terms: glo * 4(-3 + 5x) + -1log(4)(9 + -1x) = 3 Reorder the terms for easier multiplication: 4glo(-3 + 5x) + -1log(4)(9 + -1x) = 3 (-3 * 4glo + 5x * 4glo) + -1log(4)(9 + -1x) = 3 (-12glo + 20glox) + -1log(4)(9 + -1x) = 3 Reorder the terms for easier multiplication: -12glo + 20glox + -1 * 4glo(9 + -1x) = 3 Multiply -1 * 4 -12glo + 20glox + -4glo(9 + -1x) = 3 -12glo + 20glox + (9 * -4glo + -1x * -4glo) = 3 -12glo + 20glox + (-36glo + 4glox) = 3 Reorder the terms: -12glo + -36glo + 20glox + 4glox = 3 Combine like terms: -12glo + -36glo = -48glo -48glo + 20glox + 4glox = 3 Combine like terms: 20glox + 4glox = 24glox -48glo + 24glox = 3 Solving -48glo + 24glox = 3 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -3 + -48glo + 24glox = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -48glo + 24glox = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -16glo + 8glox) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -16glo + 8glox)' equal to zero and attempt to solve: Simplifying -1 + -16glo + 8glox = 0 Solving -1 + -16glo + 8glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -16glo + 1 + 8glox = 0 + 1 Reorder the terms: -1 + 1 + -16glo + 8glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -16glo + 8glox = 0 + 1 -16glo + 8glox = 0 + 1 Combine like terms: 0 + 1 = 1 -16glo + 8glox = 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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