QUIZ MATHS Pakai cara Pilih salah satu saja

QUIZ MATHS
Pakai cara
Pilih salah satu saja

QUIZ MATHS
Pakai cara
Pilih salah satu saja

Jawab:

Penjelasan dengan langkah-langkah:

$frac{1}{^alogb}+frac{1}{^bloga}=sqrt{1229}\\^bloga+^alogb=sqrt{1229}\\(^bloga+^alogb)^2=(sqrt{1229})^2\\^blog^2a+2^bloga.^alogb+^alog^2b=1229\\^blog^2a+2^blogb+^alog^2b=1229\\^blog^2a+2+^alog^2b=1229\\^blog^2a+^alog^2b=1227\\\misal~:\\frac{1}{^{ab}logb}-frac{1}{^{ab}loga}=k\\^blogab-^alogab=k\^bloga+^blogb-(^aloga+^alogb)=k\\^bloga+1-1-^alogb=k\\^bloga-^alogb=k\\(^bloga-^alogb)^2=k^2\\^blog^2a-2^bloga.^alogb+^alog^2b=k^2\\^blog^2a+^alog^2b-2=k^2$

$\1227-2=k^2\\k^2=1225\\k=sqrt{1225}\\k=35\\\maka~frac{1}{^{ab}logb}-frac{1}{^{ab}loga}=35$

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Misal :

a'log b = x → b'log a = 1/x

(x + 1/x)² = (√1229)²

x² + 1/x² = 1229 – 2 = 1227

(1/x – x)² = x² + 1/x² – 2 = 1225

1/(ab)'log b – 1/(ab)'log a

= b'log ab – a'log ab

= (b'log a + 1) – (1 + a'log b)

= b'log a – a'log b

= 1/x – x

= √1225

= 35