Q63 / 180 · COMEDK 2016 · Mathematics
If $\log _{4} 2+\log _{4} 4+\log _{4} 16+\log _{4} x=6$, then $x=$
- Correct answerA32
- B8
- C4
- D64
Solution
We have,
$\log _{4} 2+\log _{4} 4+\log _{4} 16+\log _{4} x=6$
$\log _{4}(2 \times 4 \times x \times 16)=6$
$\log _{4}(128 x)=6$
$\Rightarrow \quad 128 x=4^{6}$
$\Rightarrow \quad 128 x=64 \times 4^{3}$
$\Rightarrow \quad 2 x=4^{3}$
$\Rightarrow \quad x=\frac{64}{2}=32$
Hence, the correct answer is option: 'A'.