Question

If $(lo{g}_{10}x{)}^2-4|lo{g}_{10}x|+3=0$, the product of roots of the equation is :

• A. $3$
• B. ${10}^4$
• C. ${10}^6$
• D. $1$

Answer 1

The correct option is D $1$

Let $|{\log }_{10}x|=t$

$\therefore$ equation will become

$t^2-4t+3=0$

$t^2-t-3t+3=0(t-1)(t-3)=0$

$\therefore |{\log }_{10}x|=1,3⟹{\log }_{10}x=\pm 1,\pm 3$

$x=10,{10}^3,{10}^{-1},{10}^{-3}$

Hence, product of roots $=10\times {10}^3\times {10}^{-1}\times {10}^{-3}=1$