log2x*log4x*log8x*log16x=2/3

Đáp án:

\(\left[ \matrix{
x = 4 \hfill \cr
x = {1 \over 4} \hfill \cr} \right.\)

Giải thích các bước giải:

\(\eqalign{
& {\log _2}x.lo{g_4}x + {\log _8}x.{\log _{16}}x = {2 \over 3}\,\,\left( {x > 0} \right) \cr
& \Leftrightarrow {\log _2}x.{\log _{{2^2}}}x.{\log _{{2^3}}}x.{\log _{{2^4}}}x = {2 \over 3} \cr
& \Leftrightarrow {\log _2}x.{1 \over 2}{\log _2}x.{1 \over 3}{\log _2}x.{1 \over 4}{\log _2}x = {2 \over 3} \cr
& \Leftrightarrow {1 \over {24}}\log _2^4x = {2 \over 3} \cr
& \Leftrightarrow \log _2^4x = 16 \cr
& \Leftrightarrow \left[ \matrix{
{\log _2}x = 2 \hfill \cr
{\log _2}x = – 2 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{
x = 4 \hfill \cr
x = {1 \over 4} \hfill \cr} \right.\,\,\left( {tm} \right) \cr} \)