Pertanyaan

Tentukan nilai logaritma berikut! a. 3 lo g 6 × lo g 3 lo g 2 2 + lo g 3 + lo g 18

Tentukan nilai logaritma berikut!

a. $\frac{lo g 2 2 + lo g 3 + lo g 18}{^{3} lo g 6 \times lo g 3}$

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Habis dalam

Klaim

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

.

$fraction numerator log space 2 square root of 2 plus log space square root of 3 plus log space 18 over denominator space cubed log space square root of 6 cross times log space 3 end fraction equals 5$ .

Pembahasan

Ingat, sifat logaritma Sehingga Dengan demikian, .

Ingat, sifat logaritma

$table attributes columnalign right center left columnspacing 0px end attributes row cell space to the power of a log space b cross times to the power of a log space c equals to the power of a log space open parentheses b c close parentheses to the power of a to the power of n end exponent log space b to the power of m end cell equals cell m over n cross times to the power of a l o g space b to the power of a log space b equals fraction numerator space to the power of p log space b over denominator space to the power of p log space a end fraction end cell end table$

Sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator log space 2 square root of 2 plus log space square root of 3 plus log space 18 over denominator space cubed log space square root of 6 cross times log space 3 end fraction end cell equals cell fraction numerator log space open parentheses 2 square root of 2 cross times square root of 3 cross times 18 close parentheses over denominator log space 3 cross times cubed log space square root of 6 end fraction end cell row blank equals cell fraction numerator log space open parentheses 32 square root of 6 close parentheses over denominator log space square root of 6 end fraction end cell row blank equals cell fraction numerator log space open parentheses 36 square root of 6 close parentheses over denominator log space square root of 6 end fraction end cell row blank equals cell fraction numerator log space open parentheses 6 to the power of begin display style 5 over 2 end style end exponent close parentheses over denominator log space 6 to the power of begin display style 1 half end style end exponent end fraction end cell row blank equals cell space to the power of 6 to the power of 1 half end exponent end exponent log space 6 to the power of 5 over 2 end exponent end cell row blank equals cell fraction numerator 5 over 2 over denominator 1 half end fraction cross times space to the power of 6 log space 6 end cell row blank equals cell fraction numerator 5 over 2 over denominator 1 half end fraction cross times 1 end cell row blank equals cell fraction numerator 5 cross times 2 over denominator 2 cross times 1 end fraction end cell row blank equals 5 end table$

Dengan demikian, $fraction numerator log space 2 square root of 2 plus log space square root of 3 plus log space 18 over denominator space cubed log space square root of 6 cross times log space 3 end fraction equals 5$ .