Question

solve log 2 x square - 5 x + 14 is equal to 3​

Answer 1

I got the job done today I will see you guys at home tomorrow morning and I can get the

Answer 2

Here we go,

$log(2 {x}^{2} - 5x + 14 ) = 3 \\ \\ log(2 {x}^{2} - 5x + 14) = log(1000) \\ \\ 2 {x}^{2} - 5x + 14 = 1000 \\ \\ 2 {x}^{2} - 5x + 14 - 1000 = 0 \\ \\ 2 {x}^{2} - 5x - 986 = 0$


Now all you gotta do is solve this quadratic equation,


$2 {x}^{2} - 34x + 29x - 986 = 0 \\ \\ 2x(x - 17) + 29(x - 17) = 0 \\ \\ (2x + 29)(x - 17) = 0$


So one of the values must be 0 to get RHS = 0.

The roots we get then are,

$2x + 29 = 0 \\ 2x = - 29 \\ x = \frac{ - 29}{2}$

and

$x - 17 = 0 \\ x = 17$


Since logarithms aren't defined for -ve values.
The positive value is taken into consideration and hence x = 17.