Fatima N

14 Januari 2023 10:00

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Fatima N

14 Januari 2023 10:00

Pertanyaan

²log8 + ³log9 + ⁴log64 = ....

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P. Vidya

Mahasiswa/Alumni Universitas Negeri Malang

31 Januari 2023 08:49

<p>Halo Fatima. Kakak bantu jawab ya.</p><p>Jawab: 8</p><p>Pembahasan:</p><p>Ingat!</p><ul><li><sup>a</sup>log(a) = 1</li><li><sup>a</sup>log(b<sup>n</sup>) = n<sup>a</sup>log(b)</li></ul><p>Dengan menggunakan konsep di atas, diperoleh</p><p>²log8 + ³log9 + ⁴log64 = ²log(2<sup>3</sup>) + ³log(3<sup>2</sup>) + ⁴log(4<sup>3</sup>)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 3²log2 + 2³log3 +3⁴log</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= (3×1)+(2×1)+(3×1)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 3+2+3</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 8</p><p>&nbsp;</p><p><strong><u>Jadi, jawaban yang benar adalah 8.</u></strong></p>

Halo Fatima. Kakak bantu jawab ya.

Jawab: 8

Pembahasan:

Ingat!

  • alog(a) = 1
  • alog(bn) = nalog(b)

Dengan menggunakan konsep di atas, diperoleh

²log8 + ³log9 + ⁴log64 = ²log(23) + ³log(32) + ⁴log(43)

                                             = 3²log2 + 2³log3 +3⁴log

                                             = (3×1)+(2×1)+(3×1)

                                             = 3+2+3

                                             = 8

 

Jadi, jawaban yang benar adalah 8.


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