Решите неравенство [tex]log _{2} (5-x)*log _{2} (x+1) \leq log _{2} ((x^2-4x-5)^2/16)[/tex]. Created by elenasmirnova1. matematika-ru

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August 2022 1 5 Report

Решите неравенство
[tex]log _{2} (5-x)*log _{2} (x+1) \leq log _{2} ((x^2-4x-5)^2/16)[/tex]

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sweetburning $log_2(5-x)*log_2(x+1) \geq log_2((x-5)^2(x+1)^2)-4 \\ 
log_2(5-x)*log_2(x+1)-2log_2(5-x)-2log_2(x+1)+4 \leq 0 \\ 
log_2(5-x)[log_2(x+1)-2]-2[log_2(x+1)-2] \leq 0 \\ 
(log_2(x+1)-2)[log_2(5-x)-2] \leq 0 \\ 

Zeros: \\ 1) log_2(x+1)=2 \\ 
x+1=4 =\ \textgreater \ x=3; \\ \\ \\ 2) log_2(5-x)=2 \\ 5-x=4 =\ \textgreater \ x=1. \\ \\ \\ \\
5-x\ \textgreater \ 0 =\ \textgreater \ x\ \textless \ 5; \\ 
x+1\ \textgreater \ 0 =\ \textgreater \ x\ \textgreater \ -1 \\ \\ 
x \in (-1;1] \cup [3;5)
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