Pertanyaan

Jika 2 lo g 3 = x dan 5 lo g 2 = y , maka 8 lo g 75 = ... .

Jika $^{2} lo g 3 = x$ dan $^{5} lo g 2 = y$ , maka $^{8} lo g 75 = ...$ .

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Klaim

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

diperoleh nilai .

diperoleh nilai $log presuperscript 8 space 75 equals fraction numerator 2 plus x y over denominator 3 y end fraction$ .

Pembahasan

Gunakan konsep logaritma berikut. Diketahui dan , akan ditentukan nilai . Perhatikan perhitungan berikut. Jadi, diperoleh nilai .

Gunakan konsep logaritma berikut.

$table attributes columnalign right center left columnspacing 2px end attributes row cell log presuperscript a space open parentheses b c close parentheses end cell equals cell log presuperscript a space b plus log presuperscript a space c end cell row cell log presuperscript a to the power of n end presuperscript space b to the power of m end cell equals cell m over n space log presuperscript a space b end cell row cell log presuperscript a space b end cell equals cell fraction numerator 1 over denominator log presuperscript b space a end fraction end cell end table$

Diketahui log presuperscript 2 space 3 equals x dan log presuperscript 5 space 2 equals y , akan ditentukan nilai log presuperscript 8 space 75 .

Perhatikan perhitungan berikut.

$table attributes columnalign right center left columnspacing 2px end attributes row cell log presuperscript 8 space 75 end cell equals cell log presuperscript 8 space open parentheses 25 cross times 3 close parentheses end cell row blank equals cell log presuperscript 8 space 25 plus log presuperscript 8 space 3 end cell row blank equals cell log presuperscript 2 cubed end presuperscript space 5 squared plus log presuperscript 2 cubed end presuperscript space 3 end cell row blank equals cell 2 over 3 space log presuperscript 2 space 5 plus 1 third space log presuperscript 2 space 3 end cell row blank equals cell 2 over 3 cross times fraction numerator 1 over denominator log presuperscript 5 space 2 end fraction plus 1 third log presuperscript 2 space 3 end cell row blank equals cell 2 over 3 times 1 over y plus 1 third times x end cell row blank equals cell fraction numerator 2 over denominator 3 y end fraction plus x over 3 end cell row blank equals cell fraction numerator 2 plus x y over denominator 3 y end fraction end cell row cell log presuperscript 8 space 75 end cell equals cell fraction numerator x y plus 2 over denominator 3 y end fraction end cell end table$

Jadi, diperoleh nilai $log presuperscript 8 space 75 equals fraction numerator 2 plus x y over denominator 3 y end fraction$ .