(log9 - log3) / (log8 - log2)

Sure, let's solve this step by step:

The given expression is (log9 - log3) / (log8 - log2)

We know that log(a) - log(b) = log(a/b). So, we can rewrite the expression as:

log(9/3) / log(8/2)

This simplifies to:

log(3) / log(4)

Now, we know that log_b(a) = 1 / log_a(b). So, we can rewrite the expression as:

1 / log_3(4)

So, the simplified form of the given expression is 1 / log_3(4).