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Simplifying Log[5](6x + -14) = 1 + Log[5](x + -2) Reorder the terms: goL * 5(-14 + 6x) = 1 + Log[5](x + -2) Reorder the terms for easier multiplication: 5goL(-14 + 6x) = 1 + Log[5](x + -2) (-14 * 5goL + 6x * 5goL) = 1 + Log[5](x + -2) (-70goL + 30goxL) = 1 + Log[5](x + -2) Reorder the terms: -70goL + 30goxL = 1 + goL * 5(-2 + x) Reorder the terms for easier multiplication: -70goL + 30goxL = 1 + 5goL(-2 + x) -70goL + 30goxL = 1 + (-2 * 5goL + x * 5goL) -70goL + 30goxL = 1 + (-10goL + 5goxL) Solving -70goL + 30goxL = 1 + -10goL + 5goxL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '10goL' to each side of the equation. -70goL + 10goL + 30goxL = 1 + -10goL + 10goL + 5goxL Combine like terms: -70goL + 10goL = -60goL -60goL + 30goxL = 1 + -10goL + 10goL + 5goxL Combine like terms: -10goL + 10goL = 0 -60goL + 30goxL = 1 + 0 + 5goxL -60goL + 30goxL = 1 + 5goxL Add '-5goxL' to each side of the equation. -60goL + 30goxL + -5goxL = 1 + 5goxL + -5goxL Combine like terms: 30goxL + -5goxL = 25goxL -60goL + 25goxL = 1 + 5goxL + -5goxL Combine like terms: 5goxL + -5goxL = 0 -60goL + 25goxL = 1 + 0 -60goL + 25goxL = 1 Reorder the terms: -1 + -60goL + 25goxL = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -60goL + 25goxL = 0 The solution to this equation could not be determined.
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