Pertanyaan

Hasil adalah ....

Hasil $begin mathsize 14px style fraction numerator log presubscript space presuperscript square root of 3 end presuperscript space 5. space log presubscript space presuperscript 25 invisible function application space 3 square root of 3 minus log presubscript space presuperscript 4 invisible function application space 16 over denominator log presubscript space presuperscript 3 invisible function application space 54 minus log presubscript space presuperscript 3 invisible function application space 2 end fraction end style$ adalah ....

S. Indah

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Ingat! a q lo g b p = q p a lo g b a lo g b . b lo g a = 1 a lo g a = 1 a lo g b − a lo g c = a lo g c b Sederhanakan bentuk logaritma menjadi basis terendah kemudian gunakan sifat logaritma untuk menyederhanakannya. 3 log 5 ∙ 25 log 3 3 - 4 log 16 3 log 54 - 3 log 2 Oleh karena itu, jawaban yang benar adalah B.

Ingat!

$_{a^{q}} lo g b^{p} = \frac{p}{q}_{a} lo g b_{a} lo g b ._{b} lo g a = 1_{a} lo g a = 1_{a} lo g b -_{a} lo g c =_{a} lo g \frac{b}{c}$

Sederhanakan bentuk logaritma menjadi basis terendah kemudian gunakan sifat logaritma untuk menyederhanakannya.

$space space space fraction numerator log presubscript blank presuperscript square root of 3 end presuperscript space 5. space log presubscript blank presuperscript 25 invisible function application space 3 square root of 3 minus log presubscript blank presuperscript 4 invisible function application space 16 over denominator log presubscript blank presuperscript 3 invisible function application space 54 minus log presubscript blank presuperscript 3 invisible function application space 2 end fraction equals fraction numerator log presubscript blank presuperscript 3 to the power of 1 half end exponent end presuperscript invisible function application space 5. log presubscript blank presuperscript 5 squared end presuperscript invisible function application space 3 to the power of 3 over 2 end exponent minus log presubscript blank presuperscript 2 squared end presuperscript space invisible function application 2 to the power of 4 over denominator log presubscript blank presuperscript 3 invisible function application space 2.3 cubed minus log presubscript blank presuperscript 3 invisible function application space 2 end fraction equals fraction numerator log presubscript blank presuperscript 3 to the power of 1 half end exponent end presuperscript invisible function application space 5. log presubscript blank presuperscript 5 squared end presuperscript invisible function application space 3 to the power of 3 over 2 end exponent minus log presubscript blank presuperscript 2 squared end presuperscript invisible function application space 2 to the power of 4 over denominator log presubscript blank presuperscript 3 invisible function application space 2.3 cubed minus log presubscript blank presuperscript 3 space invisible function application 2 end fraction equals fraction numerator fraction numerator 1 over denominator 1 half end fraction log presubscript blank presuperscript 3 invisible function application space 5. fraction numerator 3 over 2 over denominator 2 end fraction space log presubscript blank presuperscript 5 space invisible function application 3 minus 4 over 2 space log presubscript blank presuperscript 2 space invisible function application 2 over denominator log presubscript blank presuperscript 3 space invisible function application fraction numerator 2.3 cubed over denominator 2 end fraction end fraction equals fraction numerator 3 over 2 space log presubscript blank presuperscript 3 invisible function application space 5. log presubscript blank presuperscript 5 invisible function application space 3 minus 2 log presubscript blank presuperscript 2 invisible function application space 2 over denominator log presubscript blank presuperscript 3 invisible function application space 3 cubed end fraction equals fraction numerator 3 over 2 minus 2 over denominator 3 end fraction equals fraction numerator negative 1 half over denominator 3 end fraction equals negative 1 over 6$

Oleh karena itu, jawaban yang benar adalah B.