We are asked to evaluate the expression: $log\ 9 - log\ 8$ $log\ 81 - log\ 64$

1. Problem Description

We are asked to evaluate the expression:

$log\ 9 - log\ 8$

$log\ 81 - log\ 64$

2. Solution Steps

First, we simplify $log\ 9 - log\ 8$. Using the property $log\ a - log\ b = log\ (a/b)$, we have

$log\ 9 - log\ 8 = log\ (9/8)$

Next, we simplify $log\ 81 - log\ 64$. Using the property $log\ a - log\ b = log\ (a/b)$, we have

$log\ 81 - log\ 64 = log\ (81/64)$

We observe that $81 = 9^2$ and $64 = 8^2$. Thus, $81/64 = (9/8)^2$. Therefore,

$log\ 81 - log\ 64 = log\ (81/64) = log\ ((9/8)^2)$

Using the property $log\ a^b = b\ log\ a$, we have

$log\ ((9/8)^2) = 2\ log\ (9/8)$

Therefore we have:

$log\ 9 - log\ 8 = log\ (9/8)$

$log\ 81 - log\ 64 = 2\ log\ (9/8)$

3. Final Answer

$log\ 9 - log\ 8 = log(9/8)$

$log\ 81 - log\ 64 = 2log(9/8)$