What other functions look similar to a logarithmic function?

Key Takeaways

• When graphed, the logarithmic function is similar in shape to the square root function, but with a vertical asymptote as x approaches 0 from the right.
• The point (1,0) is on the graph of all logarithmic functions of the form y=logbx y = l o g b x , where b is a positive real number.

What are the two special types of logarithmic functions?

Having learned about logarithms, we can note that the base of a logarithmic function can be any number except 1 and zero. However, the other two special types of logarithms are frequently used in mathematics. These are common logarithm and natural logarithm.

What are the other real life situations related to logarithmic function?

Using Logarithmic Functions 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 exponential function is equivalent to the logarithmic function?

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.

What is the relationship between exponentials and logarithms?

Logarithms are the “opposite” of exponentials, just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs “undo” exponentials. Technically speaking, logs are the inverses of exponentials. On the left-hand side above is the exponential statement “y = bx”.

How many types of logs are there in math?

There are two types of logarithms: Common logarithm: These are known as the base 10 logarithm. It is represented as log10. Natural logarithm: These are known as the base e logarithm.

What is the difference between common logarithms and natural logarithms?

The common logarithm has base 10, and is represented on the calculator as log(x). The natural logarithm has base e, a famous irrational number, and is represented on the calculator by ln(x). The natural and common logarithm can be found throughout Algebra and Calculus.

How do functions can be applied in real life?

Functions are mathematical building blocks for designing machines, predicting natural disasters, curing diseases, understanding world economies and for keeping airplanes in the air. Functions can take input from many variables, but always give the same output, unique to that function.

What are real life applications of exponential and logarithmic functions?

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.

What is the definition of logarithmic function?

Logarithmic Function Definition. In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as. For x > 0 , a > 0, and a 1, y= log a x if and only if x = a y. Then the function is given by.

What is logarithm integration?

The logarithm is a basic function from which many other functions are built, so learning to integrate it substantially broadens the kinds of integrals we can tackle. C C will be used throughout the wiki. For this solution, we will use integration by parts:

How do you find the derivative of the logarithm function?

Remember that “the logarithm is the exponent” and you will see that a = elna. Then ax = (elna)x = exlna, and we can compute the derivative using the chain rule: d dxax = d dx(elna)x = d dxexlna = (lna)exlna = (lna)ax. The constant is simply lna. Likewise we can compute the derivative of the logarithm function logax.

Are the log and exponentiation functions mirrored on the graph?

Because the log function is the inverse of the exponentiation function, we can see that they are mirrored at the line . Have a look at the following graph, where the red function is and the purple function is and see how they are mirrored at the black line which is .

https://www.youtube.com/watch?v=ZRUWGpZHHUs