Pertanyaan

Tentukan nilai logaritma berikut! b. ( 3 lo g 45 ) 2 − ( 3 lo g 5 ) 2 3 3 l o g 2 + 3 lo g 25

Tentukan nilai logaritma berikut!

b. $\frac{3 ^{^{3} l o g 2} + ^{3} lo g 25}{( ^{3} lo g 45 ) ^{2} - ( ^{3} lo g 5 ) ^{2}}$

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Jawaban terverifikasi

Jawaban

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$fraction numerator 3 to the power of space cubed log space 2 end exponent plus space cubed log space 25 over denominator open parentheses blank cubed log space 45 close parentheses squared minus open parentheses space cubed log space 5 close parentheses squared end fraction equals 1 half$ .

Pembahasan

Ingat sifat logaritma Sehingga Jadi, .

Ingat sifat logaritma

Sehingga

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 to the power of space cubed log space 2 end exponent plus space cubed log space 25 over denominator open parentheses blank cubed log space 45 close parentheses squared minus open parentheses space cubed log space 5 close parentheses squared end fraction end cell equals cell fraction numerator 2 plus cubed log space 5 squared over denominator open parentheses blank cubed log space open parentheses 9 cross times 5 close parentheses close parentheses squared minus open parentheses space cubed log space 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 plus 2 cross times cubed log space 5 over denominator open parentheses blank cubed log space 9 plus cubed log space 5 close parentheses squared minus open parentheses space cubed log space 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 plus 2 cubed log space 5 over denominator open parentheses 2 plus cubed log space 5 close parentheses squared minus open parentheses space cubed log space 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 plus 2 cubed log space 5 over denominator 4 plus 4 cubed log space 5 plus open parentheses space cubed log space 5 close parentheses squared minus open parentheses space cubed log space 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 plus 2 cubed log space 5 over denominator 4 plus 4 cubed log space 5 end fraction end cell row blank equals cell fraction numerator 2 plus 2 cubed log space 5 over denominator 2 cross times open parentheses 2 plus 2 cubed log space 5 close parentheses end fraction end cell row blank equals cell 1 half end cell end table end style$

Jadi, $fraction numerator 3 to the power of space cubed log space 2 end exponent plus space cubed log space 25 over denominator open parentheses blank cubed log space 45 close parentheses squared minus open parentheses space cubed log space 5 close parentheses squared end fraction equals 1 half$ .