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Jika begin mathsize 14px style x greater than 0 end style dan begin mathsize 14px style y greater than 0 end style, maka begin mathsize 14px style fraction numerator 3 minus 3 log squared space x y over denominator 1 minus log space x cubed y squared plus 2 log space x square root of y end fraction equals... end style 

Pembahasan Soal:

Gunakan sifat logaritma berikut:

begin mathsize 14px style log presuperscript a space b to the power of n equals n space log presuperscript a space b log presuperscript a space b plus log presuperscript a space c equals log presuperscript a space open parentheses b c close parentheses 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 3 minus 3 log squared space x y over denominator 1 minus log space x cubed y squared plus 2 log space x square root of y end fraction end cell row blank equals cell fraction numerator 3 left parenthesis 1 minus log squared space x y right parenthesis over denominator 1 minus log space x cubed minus log space y squared plus 2 open parentheses log space x plus log space square root of y close parentheses end fraction end cell row blank equals cell fraction numerator 3 open parentheses 1 plus log space x y close parentheses open parentheses 1 minus log space x y close parentheses over denominator 1 minus 3 log space x minus 2 log space y plus 2 log space x plus 2 log space y to the power of begin display style 1 half end style end exponent end fraction end cell row blank equals cell fraction numerator 3 open parentheses 1 plus log space x y close parentheses open parentheses 1 minus open parentheses log space x plus log space y close parentheses close parentheses over denominator 1 minus log space x minus 2 log space y plus 2 cross times begin display style 1 half end style log space y end fraction end cell row blank equals cell fraction numerator 3 open parentheses 1 plus log space x y close parentheses open parentheses 1 minus log space x minus log space y close parentheses over denominator 1 minus log space x minus 2 log space y plus log space y end fraction end cell row blank equals cell fraction numerator 3 open parentheses 1 plus log space x y close parentheses open parentheses 1 minus log space x minus log space y close parentheses over denominator 1 minus log space x minus log space y end fraction end cell row blank equals cell 3 open parentheses 1 plus log space x y close parentheses end cell row blank equals cell 3 plus 3 log space x y end cell end table end style 

Jadi, diperoleh begin mathsize 14px style fraction numerator 3 minus 3 log squared space x y over denominator 1 minus log space x cubed y squared plus 2 log space x square root of y end fraction equals 3 plus 3 log space x y end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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