Pertanyaan

Tanpa menggunakan kalkulator, tentukan nilai berikut: b.

Tanpa menggunakan kalkulator, tentukan nilai berikut:

b. ${}^\sqrt2\log\;\frac1{125}\cdot{}^\frac19\log\;8\cdot{}^{25}\log\;\sqrt3$

Y. Herlanda

Master Teacher

Mahasiswa/Alumni STKIP PGRI Jombang

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari ${}^\sqrt2\log\;\frac1{125}\cdot{}^\frac19\log\;8\cdot{}^{25}\log\;\sqrt3=2\frac14$ .

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah 2 4 1 . Logaritma Ingat sifat-sifat logaritma berikut: a n lo g b m = n m ⋅ a lo g b a lo g b 1 = − ( a lo g b ) ( a lo g b ) ( b lo g c ) = a lo g c a lo g a = 1 Dengan demikian, nilai dari .

Jawaban yang benar untuk pertanyaan tersebut adalah $2 \frac{1}{4}$ .

Logaritma

Ingat sifat-sifat logaritma berikut:

$^{a^{n}} lo g b^{m} = \frac{m}{n} \cdot^{a} lo g b$
$^{a} lo g \frac{1}{b} = - (^{a} lo g b)$
$(^{a} lo g b) (^{b} lo g c) =^{a} lo g c$
$^{a} lo g a = 1$

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript square root of 2 end presuperscript space 1 over 125 times log presuperscript 1 over 9 end presuperscript space 8 times log presuperscript 25 space square root of 3 end cell equals cell log presuperscript 2 to the power of 1 half end exponent end presuperscript space 125 to the power of negative 1 end exponent times log presuperscript 9 to the power of negative 1 end exponent end presuperscript space 2 cubed times log presuperscript 5 squared end presuperscript space 3 to the power of 1 half end exponent end cell row blank equals cell log presuperscript 2 to the power of 1 half end exponent end presuperscript space 5 to the power of 3 open parentheses negative 1 close parentheses end exponent times log presuperscript 3 to the power of 2 open parentheses negative 1 close parentheses end exponent end presuperscript space 2 cubed times log presuperscript 5 squared end presuperscript space 3 to the power of 1 half end exponent end cell row blank equals cell log presuperscript 2 to the power of 1 half end exponent end presuperscript space 5 to the power of negative 3 end exponent times log presuperscript 3 to the power of negative 2 end exponent end presuperscript space 2 cubed times log presuperscript 5 squared end presuperscript space 3 to the power of 1 half end exponent end cell row blank equals cell open parentheses fraction numerator negative 3 over denominator begin display style 1 half end style end fraction close parentheses open parentheses log presuperscript 2 space 5 close parentheses times open parentheses fraction numerator 3 over denominator negative 2 end fraction close parentheses open parentheses log presuperscript 3 space 2 close parentheses times open parentheses fraction numerator begin display style 1 half end style over denominator 2 end fraction close parentheses open parentheses log presuperscript 5 space 3 close parentheses end cell row blank equals cell open square brackets open parentheses fraction numerator negative 3 over denominator begin display style 1 half end style end fraction close parentheses cross times open parentheses fraction numerator 3 over denominator negative 2 end fraction close parentheses cross times open parentheses fraction numerator begin display style 1 half end style over denominator 2 end fraction close parentheses close square brackets open square brackets open parentheses log presuperscript 2 space up diagonal strike 5 close parentheses cross times open parentheses log presuperscript up diagonal strike 5 end presuperscript space up diagonal strike 3 close parentheses cross times open parentheses log presuperscript up diagonal strike 3 end presuperscript space 2 close parentheses close square brackets end cell row blank equals cell open square brackets open parentheses negative 3 cross times 2 close parentheses cross times open parentheses negative 3 over 2 close parentheses cross times open parentheses 1 half cross times 1 half close parentheses close square brackets open parentheses log presuperscript 2 space 2 close parentheses end cell row blank equals cell open square brackets negative 6 cross times open parentheses negative 3 over 2 close parentheses cross times 1 fourth close square brackets open parentheses 1 close parentheses end cell row blank equals cell 9 cross times 1 fourth end cell row blank equals cell 9 over 4 end cell row blank equals cell 2 1 fourth end cell end table end style$

Dengan demikian, nilai dari ${}^\sqrt2\log\;\frac1{125}\cdot{}^\frac19\log\;8\cdot{}^{25}\log\;\sqrt3=2\frac14$ .