2log5=p 2log3=q nilai dari log 120 adalah

2 log 5 = p
2 log 3 = q
log 120 = 2log (4 × 5 × 3)
= 2 log 4 + 2 log 5 + 2 log 3
= 2 + p + q

gak tau salah apa bener

faktor dari 120 = 2,2,2,3,5
[tex] log_{2}(5) = p \\ log_{5}(2) = \frac{1}{p} \\ log_{3}(2) = \frac{1}{q} \\ log_{2}(3) = q \\ log_{2}(5) \times log_{3}(2) = log_{3}(5) = \frac{p}{q} \\ \\ log(120) = log(2) + log(2 ) + log(2) + log(3) + log(5) \\ = 3 log(2) + log(3) + log(5) \\ = \frac{3}{ log_{2}(10) } + \frac{1}{ log_{3}(10) } + \frac{1}{ log_{5}(10) } \\ = \frac{3}{ log_{2}(2) + log_{2}(5) } + \frac{1}{ log_{3}(2) + log_{3}(5) } + \frac{1}{ log_{5}(2) + log_{5}(5) } \\ = \frac{3}{1 + p} + \frac{1}{ \frac{1}{q} + \frac{p}{q} } + \frac{1}{ \frac{1}{p} + 1 } \\ = \frac{3}{1 + p} + \frac{q}{1 + p} + \frac{p}{1 + p} \\ = \frac{3 + p + q}{1 + p} [/tex]