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Jika  dan , maka ...

Jika begin mathsize 12px style log presuperscript p space a equals 2 end style dan size 12px log presuperscript size 12px q size 12px space size 12px 8 size 12px p size 12px equals size 12px 2, maka begin mathsize 12px style log presuperscript 2 p end presuperscript fraction numerator p q squared over denominator a end fraction equals end style...

  1. begin mathsize 12px style 3 space log presuperscript 2 space 2 p end style

  2. begin mathsize 12px style log presuperscript 2 space 2 p end style

  3. begin mathsize 12px style fraction numerator 3 over denominator log presuperscript 2 space 2 p end fraction end style

  4. begin mathsize 12px style fraction numerator 1 over denominator log presuperscript 2 space 2 p end fraction end style

  5. fraction numerator size 12px 3 over denominator size 12px log presuperscript size 12px 2 size 12px space size 12px 2 size 12px p end fraction

Jawaban:

Perhatikan definisi logaritma

begin mathsize 12px style log presuperscript g space a equals n end style jika dan hanya jika begin mathsize 12px style g to the power of n equals a end style

undefined menjadi begin mathsize 12px style p squared equals a comma space log presuperscript q space 8 p equals 2 end style menjadi begin mathsize 12px style q squared equals 8 p end style

Selesaikan persamaan yang ditanyakan

Substitusikan nilai begin mathsize 12px style p squared end style dan size 12px q to the power of size 12px 2 ke dalam begin mathsize 12px style log presuperscript 2 p end presuperscript fraction numerator p q squared over denominator a end fraction end style

size 12px p presuperscript size 12px 2 size 12px space size 12px log fraction numerator size 12px p size 12px q to the power of size 12px 2 over denominator size 12px a end fraction  size 12px equals size 12px log presuperscript size 12px 2 size 12px p end presuperscript fraction numerator size 12px p size 12px times size 12px 8 size 12px p over denominator size 12px p to the power of size 12px 2 end fraction  size 12px equals size 12px log presuperscript size 12px 2 size 12px p end presuperscript size 12px space size 12px 8  size 12px equals size 12px log presuperscript size 12px 2 size 12px p end presuperscript size 12px space size 12px 2 to the power of size 12px 3  size 12px equals size 12px 3 size 12px times size 12px log presuperscript size 12px 2 size 12px p end presuperscript size 12px space size 12px 2

Karena begin mathsize 12px style log presuperscript blank presuperscript 2 p end presuperscript end presuperscript space 2 equals fraction numerator 1 over denominator log presuperscript 2 space 2 p end fraction space m e n j a d i space 3 times fraction numerator 1 over denominator log presuperscript 2 space 2 p end fraction equals fraction numerator 3 over denominator log presuperscript 2 space 2 p end fraction end style

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