Roboguru

Tentukan Nilai dari:

Pertanyaan

Tentukan Nilai dari:

begin mathsize 14px style fraction numerator log presuperscript 5 space begin display style 1 over 25 end style cross times open square brackets log presuperscript 3 to the power of negative 1 end exponent end presuperscript space 9 to the power of 5 minus log presuperscript 2 space 3 times log presuperscript 3 space begin display style 1 over 32 end style close square brackets over denominator open parentheses log presuperscript 3 space 27 close parentheses to the power of negative 2 end exponent cross times log presuperscript 2 space 8 to the power of 6 plus log presuperscript 5 space 1 to the power of 10 end fraction end style 

Pembahasan Soal:

Gunakan sifat logaritma berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell log presuperscript a space a end cell equals 1 row cell log presuperscript a space b to the power of m end cell equals cell m space log presuperscript a space b end cell row cell log presuperscript a to the power of n end presuperscript space b to the power of m end cell equals cell m over n space log presuperscript a space b end cell row cell log presuperscript a space b times log presuperscript b space c end cell equals cell log presuperscript a space c end cell row cell log presuperscript a space 1 end cell equals 0 end table end style 

Perhatikan perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell fraction numerator log presuperscript 5 space begin display style 1 over 25 end style open square brackets log presuperscript 3 to the power of negative 1 end exponent end presuperscript space 9 to the power of 5 minus log presuperscript 2 space 3 times log presuperscript 3 space begin display style 1 over 32 end style close square brackets over denominator open parentheses log presuperscript 3 space 27 close parentheses to the power of negative 2 end exponent cross times log presuperscript 2 space 8 to the power of 6 plus log presuperscript 5 space 1 to the power of 10 end fraction end cell row blank equals cell fraction numerator log presuperscript 5 space begin display style 5 squared end style open square brackets log presuperscript 3 to the power of negative 1 end exponent end presuperscript space open parentheses 3 squared close parentheses to the power of 5 minus log presuperscript 2 space begin display style 1 over 32 end style close square brackets over denominator open parentheses log presuperscript 3 space 3 cubed close parentheses to the power of negative 2 end exponent cross times log presuperscript 2 space open parentheses 2 cubed close parentheses to the power of 6 plus 10 space log presuperscript 5 space 1 end fraction end cell row blank equals cell fraction numerator 2 space log presuperscript 5 space begin display style 5 end style open square brackets log presuperscript 3 to the power of negative 1 end exponent end presuperscript space 3 to the power of 10 minus log presuperscript 2 space begin display style 2 to the power of 5 end style close square brackets over denominator open parentheses 3 space log presuperscript 3 space 3 close parentheses to the power of negative 2 end exponent cross times log presuperscript 2 space 2 to the power of 18 plus 10 space open parentheses 0 close parentheses end fraction end cell row blank equals cell fraction numerator 2 space open parentheses 1 close parentheses open square brackets begin display style fraction numerator 10 over denominator negative 1 end fraction end style log presuperscript 3 space 3 minus 5 space log presuperscript 2 space begin display style 2 end style close square brackets over denominator open parentheses 3 space open parentheses 1 close parentheses close parentheses to the power of negative 2 end exponent cross times 18 space log presuperscript 2 space 2 plus 0 end fraction end cell row blank equals cell fraction numerator 2 space open square brackets negative 10 space open parentheses 1 close parentheses minus 5 space open parentheses 1 close parentheses close square brackets over denominator 3 to the power of negative 2 end exponent cross times 18 space open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 open square brackets negative 10 minus 5 close square brackets over denominator begin display style 1 over 3 squared end style cross times 18 end fraction end cell row blank equals cell fraction numerator 2 open square brackets negative 15 close square brackets over denominator begin display style 1 over 9 end style cross times 18 end fraction end cell row blank equals cell fraction numerator negative 30 over denominator 2 end fraction end cell row blank equals cell negative 15 end cell end table end style 

Jadi, diperoleh hasil begin mathsize 14px style fraction numerator log presuperscript 5 space begin display style 1 over 25 end style open square brackets log presuperscript 3 to the power of negative 1 end exponent end presuperscript space 9 to the power of 5 minus log presuperscript 2 space 3 times log presuperscript 3 space begin display style 1 over 32 end style close square brackets over denominator open parentheses log presuperscript 3 space 27 close parentheses to the power of negative 2 end exponent cross times log presuperscript 2 space 8 to the power of 6 plus log presuperscript 5 space 1 to the power of 10 end fraction equals negative 15 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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