# 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

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Expert Answers

baxthum8 | Certified Educator

When you evaluate any `log_(a)b`

where a > b and b > 1 we use the definition of logs, which is:

`log_(a)b = x ` is `a^(x) = b`

If `x < 0;`

then b will be less than 1, however our restrictions state that b > 1.

For instance, if `5^-1 = .2`

If x = 0, then b = 1, therefore our answer won't include 0. Also, using the same example: `5^1 = 5,`

therefore x must have a value less than 1 as 1 makes a = b, but we want a> b. For instance `5^0.9 ~~4.257`

Therefore, our correct answer would be **choice "b".**