CPM Homework Help : CALC Problem 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 $1$ ?

$\operatorname{log}_ab$

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

$\operatorname{log}_ b a$

$\operatorname{log}_ a a$

Hint:

The following Laws of Logarithms should help you:

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