Question

Tính giá trị biểu thức :

\(A=\log_{2013}\left\{\log_4\left(\log_2256\right)-\log_{0,25}\left[\log_9\left(\log_464\right)\right]\right\}\)

Answer 1

\(A=\log_{2013}\left\{\log_4\left(\log_2256\right)-\log_{0,25}\left[\log_9\left(\log_464\right)\right]\right\}=\log_{2013}\left\{\log_4\left(\log_22^8\right)-\log_{0,25}\left[\log_9\left(\log_44^3\right)\right]\right\}\)

   \(=\log_{2013}\left\{\log_48-\log_{0,25}\log_93\right\}=\log_{2013}\left\{\log_{2^2}2^2-\log_{\left(\frac{1}{2}\right)^2}\frac{1}{2}\right\}\)

   \(=\log_{2013}\left(\frac{3}{2}-\frac{1}{2}\right)=\log_{2013}1=0\)