Question

If $t=-2$, then the value of ${\log }_4\frac{t^2}{4}-2{\log }_{4}4t^4$ is

• A. $2$
• B. $-4$
• C. $-6$
• D. $0$

Answer 1

The correct option is C $-6$

Given that, $t=-2$

Let $y={\log }_4\frac{t^2}{4}-2{\log }_{4}4t^4$

$\Rightarrow y={\log }_4\frac{{(-2)}^2}{4}-2{\log }_{4}4{(-2)}^4$

$\Rightarrow y={\log }_{4}1-2{\log }_{4}4{(-2)}^4$

$\Rightarrow y=0-2{\log }_4{4}^3=-6$ .........$[\because \log a^m=m\log a,{\log }_{a}a=1,{\log }_{a}1=0]$

Ans: C