Take a look at these results

\[\log_3 2 + \log_3 5 = \log_3 10\] \[\log_2 15 - \log_2 3 = \log_2 5\] \[2\log_5 7 = \log_5 49\] \[\frac{1}{3} \log_5 64 = \log_5 4\] \[(\log_5 7) \times (\log_7 11)=\log_5 11\]

How can you change the input values so that the equations still hold?

What happens if you change the base of the logarithms?

Can you state generalised versions of these results? What conditions must the base and the inputs satisfy?