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Bentuk sederhana dari = ...

Bentuk sederhana dari $begin mathsize 12px style fraction numerator log presuperscript square root of 3 end presuperscript 100 minus log 9 minus log presuperscript 5 625 over denominator log presuperscript 2 12 minus log presuperscript 2 3 end fraction end style$ = ...

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Y. Laksmi

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Mahasiswa/Alumni Universitas Negeri Semarang

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= 2.

Pembahasan

Sifat-sifat logaritma: Jadi, = 2.

Sifat-sifat logaritma:

$begin mathsize 12px style log presuperscript a b equals fraction numerator log b over denominator log a end fraction end style$

$begin mathsize 12px style fraction numerator log presuperscript square root of 3 end presuperscript 100 minus log 9 minus log presuperscript 5 625 over denominator log presuperscript 2 12 minus log presuperscript 2 3 end fraction equals fraction numerator log presuperscript open parentheses 3 close parentheses to the power of 1 half end exponent end presuperscript 100 times log 9 minus log presuperscript 5 5 to the power of 4 over denominator log presuperscript 2 open parentheses begin display style 12 over 3 end style close parentheses end fraction equals fraction numerator 2 times log presuperscript 3 100 times log 9 minus 4 times log presuperscript 5 5 over denominator log presuperscript 2 4 end fraction equals fraction numerator log presuperscript 3 100 squared times log 9 minus 4 over denominator log presuperscript 2 2 squared end fraction equals fraction numerator begin display style fraction numerator log 10 to the power of 4 times log 9 over denominator log 3 end fraction end style minus 4 over denominator 2 times log presuperscript 2 2 end fraction equals fraction numerator log 10 to the power of 4 times log presuperscript 3 9 minus 4 over denominator 2 end fraction equals fraction numerator log 10 to the power of 4 times log presuperscript 3 3 squared minus 4 over denominator 2 end fraction equals fraction numerator 4 times 2 times log presuperscript 3 3 minus 4 over denominator 2 end fraction equals fraction numerator 8 minus 4 over denominator 2 end fraction equals 4 over 2 equals 2 end style$

Jadi, $begin mathsize 12px style fraction numerator log presuperscript square root of 3 end presuperscript 100 minus log 9 minus log presuperscript 5 625 over denominator log presuperscript 2 12 minus log presuperscript 2 3 end fraction end style$ = 2.