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Much of the power of logarithms is their usefulness in solving exponential equations.Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (p H balance, a measure of acidity and alkalinity).Let’s look at the Richter scale, a logarithmic function that is used to measure the magnitude of earthquakes.
One extra point on the Richter scale can mean a lot more shaking!
With decibels, every increase of 10 means the sound is 10 times more intense.
Logarithmic and exponential functions can be used to model real-world situations.
Logarithmic functions are very helpful when working with phenomena that have a very wide range of values, because they allow you to keep the values you actually work with in a smaller range.
Visit Stack Exchange The question is The world population in 2000 was approximately 6.08 billion. The function that models this is $$ y = 6.08(10)^$$ where y represents the population in billions and t is the time in years after 2000.
Write and solve a logarithmic equation to determine what year the world population will exceed 7.5 billion.
Exponential functions are helpful with phenomena that change very quickly, or that grow or decay by a percentage over a particular time period.
We can think of logarithmic functions as the inverse of exponents.
To find the measurement of that size earthquake on the Richter scale, you find log 3920.
A calculator gives a value of 3.5932…or 3.6, when rounded to the nearest tenth.