Question

The value of a for which $\frac{1}{{\log }_{2}a}+\frac{1}{{\log }_{3}a}+\frac{1}{{\log }_{4}a}=1$, is

• A. 9
• B. 12
• C. 18
• D. 24

Answer 1

Answer: (D)

$\frac{1}{{\log }_{2}a}+\frac{1}{{\log }_{3}a}+\frac{1}{{\log }_{4}a}=1\Rightarrow {\log }_{a}2+{\log }_{a}3+{\log }_{a}4=1$
$\Rightarrow {\log }_{a}24=1\Rightarrow a=24$