How are exponential and logarithmic functions used in real life?
Exponential and logarithmic functions are no exception! 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 (pH balance, a measure of acidity and alkalinity).
What are logarithmic and exponential functions?
Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay. This unknown exponent, y, equals logax. So you see a logarithm is nothing more than an exponent.
How do you know if a word problem is exponential?
If the growth or decay involves increasing or decreasing by a fixed number, use a linear function. The equation will look like: y = mx + b f(x) = (rate) x + (starting amount). If the growth or decay is expressed using multiplication (including words like “doubling” or “halving”) use an exponential function.
What are the impacts of the applications of exponential and logarithmic function in the society?
Three of the most common applications of exponential and logarithmic functions have to do with interest earned on an investment, population growth, and carbon dating.
How logarithms helped in making our life easier?
For example, the (base 10) logarithm of 100 is the number of times you’d have to multiply 10 by itself to get 100. The simple answer is that logs make our life easier, because us human beings have difficulty wrapping our heads around very large (or very small) numbers.
What is the difference between exponential and logarithmic functions?
The exponential function is given by ƒ(x) = ex, whereas the logarithmic function is given by g(x) = ln x, and former is the inverse of the latter. The domain of the exponential function is a set of real numbers, but the domain of the logarithmic function is a set of positive real numbers.
How do you know if a function is exponential or logarithmic?
The inverse of an exponential function is a logarithmic function. Remember that the inverse of a function is obtained by switching the x and y coordinates. This reflects the graph about the line y=x. As you can tell from the graph to the right, the logarithmic curve is a reflection of the exponential curve.