Question 1
Solve for a positive value of x .

Answer

The equation is asking for what power 2 must be raised to in order to get 512. Since can be expressed as (2 multiplied by itself 9 times), we can conclude that .

Now, let’s talk about how logarithms were used historically. They revolutionized mathematics in the 16th century by simplifying complex multiplication and division into easier addition and subtraction operations. Mathematicians like John Napier made calculations much faster and laid the groundwork for the slide rule—an analog computing device used until the advent of electronic calculators!

In the real world, logarithms have several applications beyond math class. They are fundamental in fields like biology, where they help model population growth, and in economics for understanding exponential growth or decay. Logarithmic scales, like the Richter scale for earthquakes or the pH scale for acidity, allow us to conveniently represent vast changes in size or intensity.