### Home > CALC > Chapter 2 > Lesson 2.2.4 > Problem2-98

2-98.

If $1 < a < b$, which of the following logarithmic expressions represents a value that is negative? Between $0$ and $1$? Equal to $1$? Greater than $1$?

1. $\operatorname{log}_ab$

1. $\operatorname { log } _ { b } \frac { 1 } { a }$

1. $\operatorname{log}_ b a$

1. $\operatorname{log}_ a a$

The following Laws of Logarithms should help you:

$\operatorname{log}_aa = 1$
$\operatorname{log}_ab^n = n\operatorname{log}_ab$
$\text{log }_{a}\frac{1}{b^{n}}=\text{ log }_{a}b^{-n}=-n\text{log}_{a}b$
$\operatorname{log}_a1=0$