Question

${\log }_{4}2+{\log }_{4}4+{\log }_{4}x+{\log }_{4}16=6,$ then x =

• A. 64
• B. 4
• C. 8
• D. 32

Answer 1

The correct option is D 32

We have,

${\log }_{4}2+{\log }_{4}4+{\log }_{4}x+{\log }_{4}16=6$

We know that

${\log }_{m}a+{\log }_{m}b+{\log }_{m}c={\log }_{m}abc$

Therefore,

${\log }_4(2\times 4\times x\times 16)=6$

$2\times 4\times x\times 4^2=4^6$

$2\times 4^3\times x=4^3\times 4^3$

$2\times x=4^3$

$2\times x=64$

$x=32$

Hence, this is the answer.