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Jika diketahui 2 lo g 3 = p dan 3 lo g 5 = q . Maka nilai dari adalah ....

Jika diketahui $^{2} lo g 3 = p$ dan $^{3} lo g 5 = q$ . Maka nilai dari ${}^\style{font-size:12px}8\style{font-size:12px}\log\style{font-size:12px}{30}$ adalah ....

H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Pembahasan

$begin mathsize 12px style log presuperscript 8 space 30 equals fraction numerator log space 30 over denominator log space 8 end fraction space space space space space space space space space space space space space equals begin inline style fraction numerator log presuperscript 3 3 cross times 2 cross times 5 over denominator log presuperscript 3 space 2 cubed end fraction end style space space space space space space space space space space space space space equals begin inline style fraction numerator log presuperscript 3 3 cross times log presuperscript 3 2 cross times log presuperscript 3 5 over denominator 3. log presuperscript 3 space 2 end fraction end style space space space space space space space space space space space space space equals fraction numerator 1 plus begin display style 1 over p end style plus q over denominator begin display style 3 over p end style end fraction space space space space space space space space space space space space space equals space fraction numerator begin display style fraction numerator p plus 1 plus p q over denominator p end fraction end style over denominator begin display style 3 over p end style end fraction space space space space space space space space space space space space space equals fraction numerator p plus 1 plus p q over denominator p end fraction cross times p over 3 space space space space space space space space space space space space space equals 1 third open parentheses p plus 1 plus p q close parentheses end style$