Simplified, $\log_a\sqrt{a}+\log_a(a^2)$ equals:

1. Use $\log_a M+\log_a N=\log_a(MN)$ to combine the two terms. 2. That gives $\log_a\left(\sqrt{a}\cdot a^2\right)$. 3. Write the radical as a power: $\sqrt{a}=a^{1/2}$, so the product is $a^{1/2+2}=a^{5/2}$. 4. Then $\log_a\left(a^{5/2}\right)=\dfrac52$, since $\log_a(a^k)=k$. 5. Answering $2$ drops the contribution of the square-root term entirely. _Source: NECTA CSEE 2022 Basic Mathematics 041, Question 2: Exponents, Radicals and Logarithms_