Question

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Answer 1

 

$\displaystyle\bf\\c)\\log_3\Big(3log_2\big(2log_5x\big)\Big)=1\\\\3log_2\big(2log_5x\big)=3^1\\\\3log_2\big(2log_5x\big)=3~~\Big|~:3\\\\log_2\big(2log_5x\big)=1\\\\2log_5x=2^1\\\\2log_5x=2~~\Big|~:2\\\\log_5x=1\\\\x=5^1\\\\\boxed{\bf x=5}$

 

 

Answer 2

$\it log_b a =1 \Rightarrow a=b\ \ \ \ \ \ (*)\\ \\ \\ log_3(3log_2(2log_5x))=1 \Rightarrow 3log_2(2log_5x)=3|_{:3} \Rightarrow log_2(2log_5x)=1 \Rightarrow \\ \\ \Rightarrow 2log_5x=2|_{:2} \Rightarrow log_5x=1 \Rightarrow x=5$