Question

QUIZZZ !!!
(medium)

Jika a = ³log 2 , b = ⁴log 5 ,Maka berapakah nilai dari
[tex] \frac{ log_{5}(16) + log_{9}(5) }{1 + \frac{ ln(2) }{ ln(9) } } [/tex]
........​

Answer 1

Verified answer

Jawaban:

log Aritma

³log(2) = a dan ⁴log(5) = b

⁴log(5) = b → 2²log(5) = ½ . ²log(5) = ²log(5) = 2b → ⁵log(2) = 1/2b

³log(2) . ⁴log(5) = ³log(2) . 2²log(5) = ³log(2) . ½ . ²log(5) = ½ . ³log(2).²log(5) = ½.³log(5) = ³log(5) = 2ab

.

maka:

= {log(5) 16 + log(9) 5}/{ 1 + In(2)/In(9) }

= {⁵log(16) + ⁹log(5)}/{ 1 + ⁹log(2)}

= {⁵log(2⁴) + 3²log(5)}/{ 1 + 3²log(2)}

= {4.⁵log(2) + ½ . ³log(5)} /{ 1 + ½ . ³log(2)}

= {4. ½b + ½. 2ab}/{ 1 + ½ . a}

= {2b + ab}/{ 1 + ½a}

= {2b + ab} : {1 + ½a}

= {2b + ab} : {(2 + a)/2}

= {2b + ab} x {2/(2 + a)}

= b(2 + a) x 2/(2 + a)

= 2b