diket ²log5=a ⁵log3=b maka nilai dari ¹⁵log20=?

log 5/ log 2 = a
log 5 = a log 2

log 3/ log 5 = b
log 3 = b log 5

log 20/log 15 = log 5 . 2 . 2 / log 5 . 3 = log 5 + log 2 + log 2 / log 5 + log 3 = a log 2 + 2 log 2/ a log 2 + b log 5 = log 2 (a + 2)/ a log 2 + ab log 2 = log 2 (a + 2)/ log 2 (a + ab) = (a + 2) / (a + ab

¹⁵log20 = ⁵log20 / ⁵log15
= ⁵log(2.2.5) / ⁵log(3.5)
= (⁵log2 + ⁵log2 + ⁵log5) / (⁵log3 + ⁵log5)
= (1/a + 1/a + 1) / (b + 1)
= (2/a + 1) / (b + 1) . a/a
= (2 + a) / a(b + 1)