Question

Решить неравенство:
$log_2$( $2^x$ - 1) · $log_0_,_5$($2^x^+^1$ - 2) > -2

Answer 1

$begin{array}{l} text{log}_{2}left( 2^{x}-1right) times text{log}_{2^{-1}}left( 2x-2right) >text{-2}\ -text{log}_{2}text{(2}^{x}-1text{+2}^{x}-2)>-2\ text{log}_{2}left( 2^{x+1}-3right) <2text{log}_{2}2\ 2^{x+1}-3<4\ 2^{x+1}-2^{1}-2^{0}<2^{2}\ x+1-1-0<2.\ x<2. end{array}$