Log 1

The number we multiply is called the "base", so we can say: • "the logarithm of 8 with base 2 is 3" • or "log base 2 of 8 is 3" • or "the base-2 log of 8 is 3" Notice we are dealing with three numbers: • the base: the number we are multiplying (a "2" in the example above) • how often to use it in a multiplication (3 times, which is the logarithm) • The number we want to get (an "8") More Examples The exponent says how many times to use the number in a multiplication. In this example: 2 3 = 2 × 2 × 2 = 8 (2 is used 3 times in a multiplication to get 8) So a logarithm answers a question like this: In this way: The logarithm tells us what the exponent is! In that example the "base" is 2 and the "exponent" is 3: So the logarithm answers the question: Example: What is log 3(81) ... ? 3 4 = 81 So an exponent of 4 is needed to make 3 into 81, and: log 3(81) = 4 Common Logarithms: Base 10 Sometimes a logarithm is written without a base, like this: log(100) This usually means that the base is really 10. It is called a "common logarithm". Engineers love to use it. On a calculator it is the "log" button. It is how many times we need to use 10 in a multiplication, to get our desired number. Example: log(1000) = log 10(1000) = 3 Natural Logarithms: Base "e" Another base that is often used is This is called a "natural logarithm". Mathematicians use this one a lot. On a calculator it is the "ln" button. It is how many times we need to use "e" in a multiplication, to get our desired numbe...

= Related What is Log? The logarithm, or log, is the inverse of the mathematical operation of e. log 2, the x = b y; then y = log bx; where b is the base Each of the mentioned bases is typically used in different applications. Base 10 is commonly used in science and engineering, base e in math and physics, and base 2 in computer science. Basic Log Rules When the argument of a logarithm is the product of two numerals, the logarithm can be re-written as the addition of the logarithm of each of the numerals. log b(x × y) = log bx + log by EX: log(1 × 10) = log(1) + log(10) = 0 + 1 = 1 When the argument of a logarithm is a fraction, the logarithm can be re-written as the subtraction of the logarithm of the numerator minus the logarithm of the denominator. log b(x / y) = log bx - log by EX: log(10 / 2) = log(10) - log(2) = 1 - 0.301 = 0.699 If there is an exponent in the argument of a logarithm, the exponent can be pulled out of the logarithm and multiplied. log bx y = y × log bx EX: log(2 6) = 6 × log(2) = 1.806 It is also possible to change the base of the logarithm using the following rule. log b(x) = log k(x) log k(b) EX: log 10(x) = log 2(x) log 2(10) To switch the base and argument, use the following rule. log b(c) = 1 log c(b) EX: log 5(2) = 1 log 2(5) Other common logarithms to take note of include: log b(1) = 0 log b(b) = 1 log b(0) = undefined lim x→0+log b(x) = - ∞ ln(e x) = x

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• In Mathematics, most of the researchers used logarithms to transform multiplication and division problems into addition and subtraction problems before the concept of calculus came into the picture. • Logarithms are continuously used in Mathematics and Science as both subjects contend with large numbers. • In this article, we will discuss the log 1 value (log 1 is equal to zero) and the method to derive the value of log 1 through common logarithm functions and natural logarithm functions. A logarithm is an inverse expression of an exponent. For example, n = b x , where n is a real positive number. And x is the exponent number. Then, the log base format of this is Logb n = x. What are Logarithmic Functions? • A logarithm is defined as the exponent or power to which a base must be raised to get some new number. It is a convenient approach to express large numbers. • Through logarithm, the multiplication of large numbers we can easily resolve speedily. Some common properties of logarithm which proved multiplication and division of logarithms can even be written in the form of logarithm of addition or subtraction. Let’s take an example, 2 3 =8 , where 3 is the logarithm of 8 to base 2 or can be written as 3= log 2 8. Similarly, 10 2 = 100 which can be written as 2 = log 10 100 Common or Briggsian logarithm is the logarithm with base 10. Properties of Logarithm- Given below are the four basic properties of logarithm which would help you to resolve problems based on logarithm....

Step 1: Enter the logarithmic expression below which you want to simplify. The logarithm calculator simplifies the given logarithmic expression by using the laws of logarithms. Step 2: Click the blue arrow to submit. Choose "Simplify/Condense" from the topic selector and click to see the result in our Examples Popular Problems log 2 ( 6 4 ) - log ( x - 5 ) + 3 log ( x 2 + 1 ) log ( 5 ) + log ( 2 ) log 2 ( 8 ) log ( 2 ) + log ( 5 )

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What is the logarithm of one? What is the logarithm of one? log b(1) = ? The logarithmic function y = log b( x) is the inverse function of the exponential function x = b y The logarithm of x=1 is the number y we should raise the base b to get 1. The base b raised to the power of 0 is equal to 1, b 0 = 1 So base b logarithm of one is zero: log b(1) = 0 For example, the base 10 logarithm of 1: Since 10 raised to the power of 0 is 1, 10 0 = 1 Then the base 10 logarithm of 1 is 0. log 10(1) = 0 See also • • • • • •

Logarithm Rules The base b logarithm of a number is the exponent that we need to raise the base in order to get the number. • • • • • • • When b is raised to the power of y is equal x: b y = x Then the base b logarithm of x is equal to y: log b( x) = y For example when: 2 4 = 16 Then log 2(16) = 4 Logarithm as inverse function of exponential function The logarithmic function, y = log b( x) is the inverse function of the exponential function, x = b y So if we calculate the exponential function of the logarithm of x (x>0), f ( f -1( x)) = b log b ( x) = x Or if we calculate the logarithm of the exponential function of x, f -1( f ( x)) = log b( b x) = x Natural logarithm (ln) ln( x) = log e( x) When or See: Inverse logarithm calculation The inverse logarithm (or anti logarithm) is calculated by raising the base b to the logarithm y: x = log -1( y) = b y Logarithmic function The logarithmic function has the basic form of: f ( x) = log b( x) Rule name Rule log b( x ∙ y) = log b( x) + log b( y) log b( x / y) = log b( x) - log b( y) log b( x y) = y ∙log b( x) log b( c) = 1 / log c( b) log b( x) = log c( x) / log c( b) f ( x) = log b( x) ⇒ f ' ( x) = 1 / ( x ln( b) ) ∫ log b( x) dx = x ∙( log b( x) - 1 / ln( b) ) + C log b( x) is undefined when x≤ 0 log b(0) is undefined log b(1) = 0 log b( b) = 1 lim log b( x) = ∞, when x→∞ See: The logarithm of the multiplication of x and y is the sum of logarithm of x and logarithm of y. log b( x ∙ y) = log b( x) + log b( y) For example: log 10...

The number we multiply is called the "base", so we can say: • "the logarithm of 8 with base 2 is 3" • or "log base 2 of 8 is 3" • or "the base-2 log of 8 is 3" Notice we are dealing with three numbers: • the base: the number we are multiplying (a "2" in the example above) • how often to use it in a multiplication (3 times, which is the logarithm) • The number we want to get (an "8") More Examples The exponent says how many times to use the number in a multiplication. In this example: 2 3 = 2 × 2 × 2 = 8 (2 is used 3 times in a multiplication to get 8) So a logarithm answers a question like this: In this way: The logarithm tells us what the exponent is! In that example the "base" is 2 and the "exponent" is 3: So the logarithm answers the question: Example: What is log 3(81) ... ? 3 4 = 81 So an exponent of 4 is needed to make 3 into 81, and: log 3(81) = 4 Common Logarithms: Base 10 Sometimes a logarithm is written without a base, like this: log(100) This usually means that the base is really 10. It is called a "common logarithm". Engineers love to use it. On a calculator it is the "log" button. It is how many times we need to use 10 in a multiplication, to get our desired number. Example: log(1000) = log 10(1000) = 3 Natural Logarithms: Base "e" Another base that is often used is This is called a "natural logarithm". Mathematicians use this one a lot. On a calculator it is the "ln" button. It is how many times we need to use "e" in a multiplication, to get our desired numbe...

• In Mathematics, most of the researchers used logarithms to transform multiplication and division problems into addition and subtraction problems before the concept of calculus came into the picture. • Logarithms are continuously used in Mathematics and Science as both subjects contend with large numbers. • In this article, we will discuss the log 1 value (log 1 is equal to zero) and the method to derive the value of log 1 through common logarithm functions and natural logarithm functions. A logarithm is an inverse expression of an exponent. For example, n = b x , where n is a real positive number. And x is the exponent number. Then, the log base format of this is Logb n = x. What are Logarithmic Functions? • A logarithm is defined as the exponent or power to which a base must be raised to get some new number. It is a convenient approach to express large numbers. • Through logarithm, the multiplication of large numbers we can easily resolve speedily. Some common properties of logarithm which proved multiplication and division of logarithms can even be written in the form of logarithm of addition or subtraction. Let’s take an example, 2 3 =8 , where 3 is the logarithm of 8 to base 2 or can be written as 3= log 2 8. Similarly, 10 2 = 100 which can be written as 2 = log 10 100 Common or Briggsian logarithm is the logarithm with base 10. Properties of Logarithm- Given below are the four basic properties of logarithm which would help you to resolve problems based on logarithm....