Question

Giải pt sau :  

Answer 1

\(pt\Leftrightarrow\log_2\left(2^x-1\right)\left[\log_22\left(2^x-1\right)\right]=12\)

\(\Leftrightarrow\log_2\left(2^x-1\right)\left[1+\log_2\left(2^x-1\right)\right]=12\)

\(\Leftrightarrow\log_2\left(2^x-1\right)+\left[\log_2\left(2^x-1\right)\right]^2=12\)

\(t=\log_2\left(2^x-1\right)>0\Leftrightarrow pt\Leftrightarrow t^2+t=12\Leftrightarrow t=3\)

\(\Leftrightarrow\log_2\left(2^x-1\right)=3\Leftrightarrow2^x=9\Leftrightarrow x=\log_29\left(tm\right)\)