Question

If ${\log }_{a}b=2,{\log }_{b}c=3$ and ${\log }_{4}c={\log }_{4}a+5$, then $(a+b)$ is equal to

• A. 20
• B. 10
• C. 30
• D. 6

Answer 1

Answer: (A)

$b=a^2\text{ and }c=b^3=a^6$
$\therefore {\log }_4{a}^6={\log }_{4}a+5\Rightarrow 5{\log }_{4}a=5\Rightarrow a=4$
$\therefore b=16$
$\therefore a+b=20$