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  4. The value of a for which (1/ log 2 a)+(1/ log 3 a)+(1/ log 4 a)=1, is

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Q. The value of a for which $\frac{1}{\log _2 a}+\frac{1}{\log _3 a}+\frac{1}{\log _4 a}=1$, is

Continuity and Differentiability

Solution:

$ \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$
$\Rightarrow \log _{ a } 24=1 \Rightarrow a =24$