Solve:log_2x+log_4x+log_16x=21/4
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Solve: log_2x+log_4x+log_{16}x=frac{21}{4}

JEE/Engineering Exams
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Solve:log_2x+log_4x+log_16x=21/4
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@log_2x+log_4x+log_{16}x=frac{21}{4} ⇒frac{logx}{log2}+frac{logx}{log4}+frac{logx}{log16} =frac{21}{4} ⇒frac{logx}{log2}+frac{logx}{2log2}+frac{logx}{4log2}=frac{21}{4} ⇒(1+frac{1}{2}+frac{1}{4}) log_2x=frac{21}{4} ⇒(frac{4+2+1}{4}) log_2x=frac{21}{4} ⇒log_2x=3 ⇒x=2^3=8x=8

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