Change using the change-of-base formula with a calculator.
Round to 4 decimal places.

To change using the change-of-base formula, you can use either the natural logarithm or common logarithm. The formula is:

Using common logarithms (base 10), it would be:

Using a calculator, you find:

and .

Thus,

So, rounded to four decimal places, .

Did you know that logarithms were first popularized by Scottish mathematician John Napier in the early 17th century? He introduced logarithmic concepts to simplify calculations, especially multiplication and division, which were quite tedious before the advent of calculators!

In real-world applications, logarithms are used extensively in fields like finance and science. For instance, they help in measuring sound intensity (decibels), earthquake intensity (Richter scale), and even in determining the pH level of a solution. They allow us to manage and interpret vast ranges of values in a more digestible format!