Expand log base 3 of (9 times x to the fifth) as far as possible.

1. The argument is a product, so the product rule splits it into two logarithms added. 2. That gives log base 3 of 9 plus log base 3 of x to the fifth. 3. The power rule moves the exponent 5 in front of the second logarithm. 4. That turns the second piece into 5 times log base 3 of x. 5. The first piece can be evaluated, since 3 squared is 9, so log base 3 of 9 is 2. 6. Putting the pieces together gives 2 plus 5 log base 3 of x. 7. Answering 9 plus 5 log base 3 of x leaves the first logarithm unevaluated and drops its logarithm sign. 8. Answering 2 times 5 log base 3 of x uses a product where the product rule demands a sum. 9. Answering 5 plus 2 log base 3 of x swaps the two numbers, applying the exponent to the wrong factor. _Source: OpenStax Precalculus (CC BY 4.0), section 4.5 Logarithmic Properties_