Question

Jika 7log2=a dan 3log2=b maka 6log98=…

Answer 1

7 log 2 = a

log7/log2 = a
log 2/log 7 = 1/a
2 log 7 = 1/a

3 log 2 = b
log 3/log 2 = b
log 2/log 3 = 1/b
2 log 3 = 1/b

6 log 98
= 6 log 7² × 2
= 12 log 7 × 2
= 2 log 12/ 2log 7 × 2
= 2 log 12/ 2 (log 7 + log 2)
= 2 log 2² × 3 / 2 (log 7 + log2)
= 4 (log 2 + log 3) / 2 (log 7 + log 2)
= 1/2 (2log2 + 2log3) / 2log7 + 2log2
= 1/2 (1 + 1/b) / 1/a + 1
= (1/2 + 1/2b) / (1+a)/b
= (b+1)/2b × b/(1+a)
= (b+1)/(2+2a)
= ½ (b+1)/(1+a)