To solve , we can express both 8 and 64 as powers of 2. We know that and . Using the change of base formula, we rewrite the log:

So, .

Here’s a fun trivia tidbit: logarithms were invented by John Napier in the early 17th century as a mathematical tool to simplify calculations, especially multiplication and division, essentially paving the way for easier navigation and advancements in science!

Ever wondered how logarithms are practically applied in real life? They are crucial for anything that involves exponential growth or decay, such as population growth, radioactive decay, and even in smartphone algorithms that efficiently compress and store images and videos.