Question

若以2为底3的对数=a,3的b次方=7,则以42为底的56的对数是多少?

Answer 1

log(2)3=a,可得log(3)2=1/a
3^b=7,可得log(3)7=b
所以：
log(2)7=[log(3)7]/[log(3)2]=ab(换底公式)
log（42）56=[log(2)56]/[log(2)42]
=[log(2)7+3]/[log(2)7+log(2)3+1]
=(ab+3)/(ab+a+1)