Pertanyaan

Grafik fungsi y = 2 lo g x berada di atas grafik fungsi apabila ...

Grafik fungsi $y =^{2} lo g x$ berada di atas grafik fungsi y equals scriptbase log invisible function application x end scriptbase presuperscript 2 apabila ...

M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Akan ditunjukkan kondisi dimana grafik fungsi berada di atas grafik fungsi ,yang berarti bahwa . Ingat sifat-sifat pada bentuk logaritma yaitu Sehingga akan didapatkan Jadi, dapat disimpulkan bahwa grafik fungsi berada di atas grafik fungsi apabila . Oleh karena itu, jawaban yang benar adalah A.

Akan ditunjukkan kondisi dimana grafik fungsi y equals scriptbase log invisible function application x end scriptbase presuperscript 2 berada di atas grafik fungsi , yang berarti bahwa .

Ingat sifat-sifat pada bentuk logaritma yaitu

$fraction numerator scriptbase log invisible function application b end scriptbase presuperscript a over denominator scriptbase log invisible function application c end scriptbase presuperscript a end fraction equals scriptbase log invisible function application b end scriptbase presuperscript c$

Sehingga akan didapatkan

$table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application x end scriptbase presuperscript 2 end cell greater than cell scriptbase log invisible function application x end scriptbase presuperscript 3 end cell row cell scriptbase log invisible function application x end scriptbase presuperscript 2 minus scriptbase log invisible function application x end scriptbase presuperscript 3 end cell greater than 0 row cell fraction numerator log invisible function application x over denominator log invisible function application 2 end fraction minus fraction numerator log invisible function application x over denominator log invisible function application 3 end fraction end cell greater than 0 row cell fraction numerator log invisible function application x times log invisible function application 3 over denominator log invisible function application 2 times log invisible function application 3 end fraction minus fraction numerator log invisible function application x times log invisible function application 2 over denominator log invisible function application 3 times log invisible function application 2 end fraction end cell greater than 0 row cell fraction numerator log invisible function application x times log invisible function application 3 minus log invisible function application x times log invisible function application 2 over denominator log invisible function application 2 times log invisible function application 3 end fraction end cell greater than 0 row cell log invisible function application x times log invisible function application 3 minus log invisible function application x times log invisible function application 2 end cell greater than 0 row cell log invisible function application x left parenthesis log invisible function application 3 minus log invisible function application 2 right parenthesis end cell greater than 0 row cell log invisible function application x open parentheses log invisible function application 3 over 2 close parentheses end cell greater than 0 row cell log invisible function application x end cell greater than 0 row cell log invisible function application x end cell greater than cell log invisible function application 1 end cell row x greater than 1 end table$

Jadi, dapat disimpulkan bahwa grafik fungsi y equals scriptbase log invisible function application x end scriptbase presuperscript 2 berada di atas grafik fungsi apabila x greater than 1 .

Oleh karena itu, jawaban yang benar adalah A.