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(iv) Find the product of roots of the eq...

(iv) Find the product of roots of the equation `(log_3x)^2 -2(log_3x) -5 = 0`.

Text Solution

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Let `log_3x = t`
Then, our equation becomes,
`t^2-2t-5=0`
Now, roots of this quadratic equation are,
`(-(-2)+-sqrt((-2)^2-4(-5)(1)))/(2(1))`
`=(2+-sqrt24)/2 = 1+-sqrt6`
So, `t = 1+sqrt6` and `t = 1-sqrt6`
`log_3x = 1+sqrt6` and `log_3x = 1-sqrt6`
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