CPM Homework Help : APCALC 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 $1$ ?

$\log_a(b)$

$\log_b\frac{1}{a}$

$\log_b(a)$

$\log_a(a)$

Hint:

The following Laws of Logarithms should help you:

$\log_aa=1$

$\log_ab^n=n\log_ab$

$\text{log }_{a}\frac{1}{b^{n}}=\text{ log }_{a}b^{-n}=-n\text{log}_{a}b$

$\log_a1=0$