To evaluate the expression log3(a) + log3(a^3) + log3(3), we can use logarithmic properties to simplify it step by step.
1. **Using the Power Rule:** The logarithmic property logb(x^n) = n * logb(x) allows us to simplify log3(a^3) as follows:
log3(a^3) = 3 * log3(a)
2. **Adding the Logs:** Now, substituting this back into the original expression, we have:
log3(a) + 3 * log3(a) + log3(3)
This simplifies to:
4 * log3(a) + log3(3)
3. **Evaluating log3(3):** We know that logb(b) = 1, so:
log3(3) = 1
4. **Final Expression:** Now, our expression becomes:
4 * log3(a) + 1
In summary, the expression log3(a) + log3(a^3) + log3(3) simplifies to 4 * log3(a) + 1.