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Pertanyaan

Tentukan himpunan penyelesaian dari pertidaksamaan logaritma berikut:

 begin mathsize 14px style scriptbase log open parentheses x minus 3 close parentheses plus scriptbase log open parentheses x plus 3 close parentheses greater or equal than 4 end scriptbase presuperscript 2 end scriptbase presuperscript 2 end style 

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

diperoleh begin mathsize 14px style HP equals open curly brackets right enclose x space x greater or equal than 5 space close curly brackets end style.

Pembahasan

Ingat bahwa:

begin mathsize 14px style scriptbase log space f open parentheses x close parentheses plus scriptbase log space g open parentheses x close parentheses equals scriptbase log space f open parentheses x close parentheses times g open parentheses x close parentheses end scriptbase presuperscript a end scriptbase presuperscript a end scriptbase presuperscript a end style 

begin mathsize 14px style scriptbase log space b to the power of n equals n times scriptbase log space b end scriptbase presuperscript a end scriptbase presuperscript a end style.

Dengan menggunakan sifat logaritma di atas, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table attributes columnalign right center left end attributes row cell scriptbase log open parentheses x minus 3 close parentheses plus scriptbase log open parentheses x plus 3 close parentheses end scriptbase presuperscript 2 end scriptbase presuperscript 2 end cell greater or equal than 4 row cell scriptbase log open parentheses x minus 3 close parentheses open parentheses x plus 3 close parentheses end scriptbase presuperscript 2 end cell greater or equal than cell 4 times scriptbase log space 2 end scriptbase presuperscript 2 end cell row cell scriptbase log open parentheses x squared minus 9 close parentheses end scriptbase presuperscript 2 end cell greater or equal than cell scriptbase log space 2 to the power of 4 end scriptbase presuperscript 2 end cell row cell x squared minus 9 end cell greater or equal than 16 row cell x squared minus 9 minus 16 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 minus 5 close parentheses open parentheses x plus 5 close parentheses end cell greater or equal than 0 end table end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table attributes columnalign right center left end attributes row cell x less or equal than negative 5 end cell logical or cell x greater or equal than 5 end cell end table end cell end table

Garis bilangannya sebagai berikut.

Syarat numerus

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell greater than 0 row cell x minus 3 end cell greater than 0 row x greater than 3 end table end style   dan   begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell greater than 0 row cell x plus 3 end cell greater than 0 row x greater than cell negative 3 end cell end table end style

Garis bilangannya menjadi:

Dengan demikian, diperoleh begin mathsize 14px style HP equals open curly brackets right enclose x space x greater or equal than 5 space close curly brackets end style.

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