Question

Solve log, x2–5x+14=3.​

Answer 1

$log_{10} (x^{2} - 5x + 14 ) = 3$

$\implies x^{2} - 5x + 14 = 10^{3}$

$\boxed { \pink { If \: log_{a} x = N \implies x = a^{N} ,\:x >0}}$

$\implies x^{2} - 5x + 14 = 1000$

$\implies x^{2} - 5x + 14 - 1000 = 0$

$\implies x^{2} - 5x - 986 = 0$

/* Splitting the middle term,we get */

$\implies x^{2} - 34x + 29x - 986 = 0$

$\implies x( x - 34 ) + 29( x - 34 ) = 0$

$\implies ( x - 34 )( x + 29 ) = 0$

$\implies x - 34 = 0 \: Or \: x + 29 = 0$

$\implies x = 34 \: Or \: x = -29$

Therefore.,

$\red { Value \: of \: x } \green { = 34 }$

•••♪