Evaluate :
` (log8 xx log9)/(log 27) `

Answer

To evaluate the expression \( \frac{\log 8 \times \log 9}{\log 27} \), we can follow these steps:

### Step 1: Rewrite the logarithms in terms of base 2 and base 3
We know that:
- \( 8 = 2^3 \)
- \( 9 = 3^2 \)
- \( 27 = 3^3 \)

Thus, we can rewrite the logarithms:
\[ \log 8 = \log(2^3) \quad \text{and} \quad \log 9 = \log(3^2) \quad \text{and} \quad \log 27 = \log(3^3) \]

### Step 2: Apply the power rule of logarithms
Using the property of logarithms that states \( \log(a^n) = n \log(a) \), we can simplify:
\[ \log 8 = 3 \log 2 \]
\[ \log 9 = 2 \log 3 \]
\[ \log 27 = 3 \log 3 \]

### Step 3: Substitute back into the expression
Now substituting these values back into the original expression:
\[ \frac{\log 8 \times \log 9}{\log 27} = \frac{(3 \log 2) \times (2 \log 3)}{3 \log 3} \]

### Step 4: Simplify the expression
Now we can simplify:
\[ = \frac{6 \log 2 \log 3}{3 \log 3} \]

### Step 5: Cancel out common terms
The \( \log 3 \) in the numerator and denominator cancels out:
\[ = 2 \log 2 \]

### Final Answer
Thus, the evaluated expression is:
\[ \boxed{2 \log 2} \]