Pertanyaan

Jika 2 lo g 5 = a d an 6 lo g 2 = b , maka 75 lo g 60 = ....

Jika $^{2} lo g 5 = a d an^{6} lo g 2 = b, maka^{75} lo g 60 = ....$

$fraction numerator a b plus b plus 1 over denominator 2 a b minus b plus 1 end fraction$
$fraction numerator a b minus b plus 1 over denominator 2 a b plus b plus 1 end fraction space$
$fraction numerator a b plus b minus 1 over denominator 2 a b minus b minus 1 end fraction$
$fraction numerator a b minus b minus 1 over denominator 2 a b plus b minus 1 end fraction$
$fraction numerator a b plus b plus 1 over denominator 2 a b plus b plus 1 end fraction$

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K. Anggun

Master Teacher

Jawaban terverifikasi

Pembahasan

Ingat bahwa Maka Perhatikan bahwa angka 2 dipilih karena pada keduanya mengandung angka 2. 75 lo g 60 = = = = = = = 2 l o g 75 2 l o g 60 2 l o g ( 2 5 2 ⋅ 6 ) 2 l o g ( 2 ⋅ 5 ⋅ 6 ) 2 l o g 5 2 + 2 l o g 6 − 2 l o g 2 2 l o g 2 + 2 l o g 5 + 2 l o g 6 2 ⋅ 2 l o g 5 + 6 lo g 2 1 − 2 l o g 2 2 l o g 2 + 2 l o g 5 + 6 lo g 2 1 2 ⋅ a + b 1 − 1 1 + a + b 1 2 ab + 1 − b b + ab + 1 2 ab − b + 1 ab + b + 1

Ingat bahwa

$table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a space b end cell equals cell fraction numerator log presuperscript c space b over denominator log presuperscript c space a end fraction end cell row cell log presuperscript a space b c end cell equals cell log presuperscript a space b plus log presuperscript a space c end cell row cell log presuperscript a space b over c end cell equals cell log presuperscript a space b minus log presuperscript a space c end cell row cell log presuperscript a space b to the power of c end cell equals cell c times log presuperscript a space b end cell row cell log presuperscript a space a end cell equals 1 row cell log presuperscript a space b end cell equals cell fraction numerator 1 over denominator log presuperscript b space a end fraction end cell end table$

Maka $log presuperscript 75 space 60 equals fraction numerator log presuperscript 2 space 60 over denominator log presuperscript a space 75 end fraction$

Perhatikan bahwa angka 2 dipilih karena pada keduanya mengandung angka 2.

$^{75} lo g 60 = = = = = = = \frac{^{2} l o g 60}{2 l o g 75} \frac{^{2} l o g ( 2 \cdot 5 \cdot 6 )}{^{2} l o g ( \frac{5 ^{2} \cdot 6}{2} )} \frac{^{2} l o g 2 + ^{2} l o g 5 + ^{2} l o g 6}{^{2} l o g 5 ^{2} + ^{2} l o g 6 - ^{2} l o g 2} \frac{^{2} l o g 2 + ^{2} l o g 5 + \frac{1}{^{6} lo g 2}}{2 \cdot ^{2} l o g 5 + \frac{1}{^{6} lo g 2} - ^{2} l o g 2} \frac{1 + a + \frac{1}{b}}{2 \cdot a + \frac{1}{b} - 1} \frac{b + ab + 1}{2 ab + 1 - b} \frac{ab + b + 1}{2 ab - b + 1}$