Number of solutions of the equation ${log}_{(x^{2} + 6 x + 8)} [{log}_{2 x^{2} + 2 x + 3} (x^{2} - 2 x)] = 0$ is

Open in App

Solution

${log}_{2 x^{2} + 2 x + 3} (x^{2} - 2 x) = 1 \Rightarrow 2 x^{2} + 2 x + 3 = x^{2} - 2 x$
$\Rightarrow x^{2} + 4 x + 3 = 0 \Rightarrow x = - 1, - 3$
but $x = - 4$ is not in the domain

Suggest Corrections

Similar questions

{log}_{x^{2} + 6 x + 6} ({log}_{2 x^{2} + 2 x + 3} (x^{2} - 2 x)) = 0

{log}_{x^{2} - 6 x + 8} ({log}_{{2 x}^{2} - 2 x - 8} (x^{2} + 5 x)) = 0

{log}_{(x^{2} + 6 x + 8)} ({log}_{(2 x^{2} + 2 x + 3)} (x^{2} - 2 x)) = 0

{log}_{x^{2} + 6 x + 8} {log}_{{2 x}^{2} + 2 x + 3} (x^{2} - 2 x) = 0

({log}_{2 x^{2} + 2 x + 3} (x^{2} - 2 x)) = 0

Join BYJU'S Learning Program