### Exponentials & Logarithms

Fluency exercise

 Increasing size $\longrightarrow$ Increasing size $\downarrow$ $\log_{\square} \square$ $\log_{4} 2$ $\log_4 3$ $\log_{4} 5$ $\log_{\square} \square$ $\log_{5} 3$ $1$ $\log_{3} 5$ $\log_{\square} \square$ $\log_{5} 4$ $\log_3 4$ $\log_{2} 4$ $\log_{\square} \square$
• Try to make your extra logarithms as general as possible. For instance if you want $\log_{a} 3$ to be less than $\log_{5} 3$, what conditions must $a$ satisfy?