Question

1) Dik: 2 log 3 = m dan 2 log 5 = n maka 2 log 90 adalah...
2) 5 log 9 + 3. 5 log 2 + 1/2. 5 log 25 - 2. 5 log 6 - 5 log 2 =...
3) 9 log 8 = 3m maka 3 log 2 adalah...
4) 9 log 25 x 5 log 2 - 3 log 54 =...

Answer 1

²log3 = m    
²log 5 = n.........⁵log2 = 1/n
⁵log2. ²log3 = ⁵log3 = m/n
³log5 = n/m



1.  ²log 90 = ²log (2.9.5) = ²log2 + ²log9 + ²log5 = 1+ 2.²log3 + ²log5 = 1+2m + n


no. 2
⁵log9 + 3.⁵log 2 + 1/2 ⁵log 25 - 2. ⁵log 6 - ⁵log2
   = 2.⁵log3 + 3.⁵log2 + ⁵log√25 - 2[⁵log2 + ⁵log3] - ⁵5log2
   = 2.m/n + 3/n + 1 - 2[1/n  +  m/n] - 1/n
   = 2m/n + 3/n +1 -2/n + 2m/n -1/n = 4m/n + 1 = (4m + n)/n

no.3
⁹log8 = 3m
   ³log2 = log 2/ log 3 =( log 8¹/³ ) / (log 9¹/²) = (1/3 log 8)/ (1/2 log 9) = 2/3.  ⁹log 8 = 2/3 .3m = 2m

  atau cara lain
 ³log2 =  ^9^1/2 log 8^1/3 = (1/3 : 1/2)⁹log8 = 2/3⁹log8 = 2/3 . 3m =2m


no.4
⁹log25 x ⁵log2 -  ³log64 =( log 25/ log 9) x (log2/log5) - (log 64/log3)
                                  =(2log5/ 2log3) x (log2/log5) - (6log2/log3)
                                  =( 2log2/log3) - (6log2/log3) = -4.log2/log3
                                   =³log 2⁻⁴ = ³log (1/16)