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Tentukan himpunan penyelesaian pertidaksamaan berikut: b. 41​log (x2−24)≥0

Pertanyaan

Tentukan himpunan penyelesaian pertidaksamaan berikut:

b. log presuperscript 1 fourth end presuperscript space open parentheses x squared minus 24 close parentheses greater or equal than 0 

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

himpunan penyelesaian pertidaksamaan di atas adalah open curly brackets x vertical line x less or equal than negative 5 logical or x greater or equal than 5 close curly brackets.

Pembahasan

Ingat sifat logaritma!

log presuperscript a space 1 equals 0    

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 1 fourth end presuperscript space open parentheses x squared minus 24 close parentheses end cell greater or equal than 0 row cell log presuperscript 1 fourth end presuperscript space open parentheses x squared minus 24 close parentheses end cell greater or equal than cell log presuperscript 1 fourth end presuperscript space 1 end cell row cell x squared minus 24 end cell greater or equal than 1 row cell x squared minus 24 minus 1 end cell greater or equal than 0 row cell x squared minus 25 end cell greater or equal than 0 row cell open parentheses x plus 5 close parentheses open parentheses x minus 5 close parentheses end cell greater or equal than 0 row cell x plus 5 end cell greater or equal than 0 row x greater or equal than cell negative 5 end cell row cell x minus 5 end cell greater or equal than 0 row x greater or equal than 5 end table   

Jadi, himpunan penyelesaian pertidaksamaan di atas adalah open curly brackets x vertical line x less or equal than negative 5 logical or x greater or equal than 5 close curly brackets.

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