Logarithm Questions

Even before the discovery of calculus, mathematicians employed logarithms to convert divisions and multiplications into subtraction and addition questions. To get a given number in logarithm, the power is raised to some number, which is usually a base number. You may write any exponential function in logarithmic form because logarithmic functions are the inverse of exponential functions. All logarithmic functions are expressed in exponential form in the same way. Logarithms are useful in managing numbers of a much more workable scale when working with very huge numbers.

Logarithm

An exponent expressed in a special form is called a logarithm. For instance, we know that 32=9 is a valid exponential equation. The base is 3 and the exponent is 2. We’ll define a function as 9 =2 in logarithmic notation. “The logarithm of 9 to the base 3 is 2,” we state in words. We’ve effectively dropped the exponent down to the mainstream at this point. Although this was done to make multiplication and division easier, logarithms are still extremely useful in mathematics.

fx=x  is the definition of a logarithmic function. The base of the logarithm in this case is b and base 10 are the most common bases encountered in logs to base 10 and natural logs. Many logarithmic applications exist in real life, such as electronics, earthquake research, acoustics, and population prediction.

Common logarithm function

A common logarithm is one with base 10. There are 10 bases and 10 digits from 0 to 9, and place value is established by groups of ten in our number system. With a base of 10, you can recall common logarithms.

Natural logarithmic functions

A natural logarithm is not the same as a standard logarithm. The base of a natural logarithm is number e when the base of the common logarithm is 10. Despite the fact that e is a variable, it is a fixed irrational number equal to 2.718281828459. Euler’s number or Napier’s constant are other names for e. Leonhard Euler, a mathematician, was honoured with the letter e. e appears to be a difficult number, but it is actually quite intriguing. In business, economics, and biology, the function fx=x  has several uses. As a result, e is a significant number.

Properties of logarithmic functions

Product rule:

MN=M +N 

The log of a product is equal to the sum of the logs of its elements, according to this property.

Add the exponents after multiplying two numbers with the same base.

For instance, log 20 +log 2 =log 40

Quotient rule:

MN =M -N

The log of a quotient is equal to the difference between the logs of the dividend and the divisor, according to this property.

Subtract the exponent from two numbers with the same base.

For instance, 54 -9 =549=6  =1

Power rule:

Mp =pM

The log of a power is equal to the exponent times the logarithm of the base of the power, according to this condition.

For instance, 25

=52
=25
=2×1

Logarithm questions

1. Rewrite the given logarithm equations in exponent form.

1. 36 =2
2. m =p

Solution: 36 =2

              🡺36=62

                 m =p

              🡺m=ap

1. Solve for the variables

1. 49 =y
2. 18=y

Solution: 49 =y                                  18=y

              🡺72=y                             🡺2-3 =y

              🡺27 =y                            🡺-32 =y

              🡺y=2                                        🡺y=-3

Conclusion

The logarithm functions are an important element of the mathematics curriculum. Logarithmic functions can be used in a variety of domains and for a variety of reasons. As a result, understanding this notion has become a requirement for pupils.

Calculus, exponents, and other hard mathematical ideas are made easier to understand with logarithmic functions. Logarithmic functions help you solve problems involving exponents, integrals, differentiation, and other topics while also improving your grasp of them.