SOLUTION: If X=logbase 24 12;y=logbase36 24;z=logbase48 36 then xyz+1 = ? a) 2xy b) 2zx c) 2yz

Question 973793: If X=logbase 24 12;y=logbase36 24;z=logbase48 36 then
xyz+1 = ?
a) 2xy b) 2zx c) 2yz
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Use change of base formula
log 12/log 24 =0.7819
log 24/log 36 =0.8868
log 36/log48 =0.9257
Product +1 =1.6418
2xy=1.3868
2zx=1.447
2yz= 1.6418
Alternatively,
change base to 48
[log48 (24)/log48 (12)]* log48 (36)/log48 (24) * [log 48 (36)] everything cancels but log 48 (24), and change of base formula gives same product as above.
2xy=log24 (144)*log 36 (24) =[ log 36 (144)/log 36 (24)}*log base36 (24)= log36 (144)
2yz=log36 (576)*log48 (36)= [log 48 (576)/log48 (36)] log 48 (36) =log 48 (576), etc. Think change base to 10 and solving it that way is easier.

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