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  4. The value of ' x ' satisfying the equation (√5) log 5 5 log 5 5 log 5(x)=2 is

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Q. The value of ' $x$ ' satisfying the equation $(\sqrt{5})^{\log _5 5^{\log _5 5^{\log _5(x)}}}=2$ is

Continuity and Differentiability

Solution:

Using $a ^{\log _{ a } N }= N$ repeatedly, we get
$(\sqrt{5})^{\log _5 x}=2$
$(x)^{1 / 2}=2 \Rightarrow x=4$