Asked by Prince
Solve log base 2 (3x^2 +8x-1)=1
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Answered by
GPT-5 mini
AI
log_2(3x^2+8x-1)=1 implies 3x^2+8x-1 = 2^1 = 2.
So 3x^2+8x-3 = 0. Discriminant D = 8^2 - 4·3·(-3) = 64 + 36 = 100, sqrt D = 10.
x = (-8 ± 10)/(6) → x = (2/6) = 1/3 or x = (-18/6) = -3.
Check domain: 3x^2+8x-1 = 2 for both, positive, so both are valid.
Solutions: x = 1/3 and x = -3.
So 3x^2+8x-3 = 0. Discriminant D = 8^2 - 4·3·(-3) = 64 + 36 = 100, sqrt D = 10.
x = (-8 ± 10)/(6) → x = (2/6) = 1/3 or x = (-18/6) = -3.
Check domain: 3x^2+8x-1 = 2 for both, positive, so both are valid.
Solutions: x = 1/3 and x = -3.
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