Product Property of Logarithms

Writing $\log_{3}(2)+\log_{3}(5)$ as $\log_{10}(2*5)$ mistakenly changes the base without proper conversion.

Expressing $\log_{3}(2)+\log_{3}(5)$ as $\log_{3}(2+5)$ incorrectly replaces multiplication with addition inside the logarithm.

Simplifying $\log_{3}(2)+\log_{3}(5)$ to $\log_{3}(2*5)=\log_{3}(10)$ demonstrates the logarithmic product property.

Simplifying $\log_{3}(2)+\log_{3}(5)$ to $\log_{3}(7)$ is a misapplication of the property.