When you evaluate any log (base a) b where a > b and b> 1 then: a) log (base a) b > 1 b) 0 < log (base a) b < 1 c) log (base a) b < 0 d) Cannot be determined 

Expert Answers
justaguide eNotes educator| Certified Educator

The value of `log_a b` has to be determined given that a > b and b > 1.

Expressing `log_a b` in terms of logarithms with the same base:

`log_a b = (log b)/(log a)`

As a > b > 1, log a > log b, and log a and log b are positive.

The value of `log_a b` lies between 0 and 1.

The correct answer is b.

aruv | Student

`x=log_a b`





since b>1 and a>b

therefor a>b>1

ln is an increasing fuction in `(1,oo)`




`ln(a)>0 ad ln(b)>0`




`0<log_a b<1`

THus correct answer is B