Rules For Natural Logarithms

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In this page we ar going to discuss about natural logarithm rule.The logarithm of a digit to a particular base is the exponent or power to which the base has to be increased in order to create that number.The natural logarithm rules of a function are the base is specified the e in logarithm. The irrational constant is known as the e. The natural logarithm rules are represented as ln(x), loge(x) and the value of e is contained simply log(x).

Natural logarithm rules
The natural logarithm rules function can be chosen as an actual significance function of a actual variable when it is the opposite of the exponential functions which lead to identities.

eln(y) = y if y > 0

ln(ey) = y

The method of logarithms is used to make simpler the arithmetical calculators to a large extent. By using logarithms, consequences are obtained properly to convinced decimal places.

e y = x

The e is specified the base logarithm of x is

ln(a) = loge(a) = b

The e is specified the constant otherwise Euler’s number is

e = 2.71828183

The relation between e and log is , if e x=y ...
... then log y=x

Product rule:
The rule name is product. The rule is,

logx (a.b) = logx a + logx b.

The example is,

logx (9.8) = logx 9 + logx 8.

Quotient rule:
The rule name is quotient. The rule is,

Log (a/b) = loga – logb.

The example is,

Log (10/8) = log10 – log8.

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Change of base formula:
The rule name is change of base formula. The rule is

Log ab = logb /log a.

The example is,

Log 8.2 = log8 /log 2.

Power rule:
The rule name is power. The rule is,

ln(a b) = b ? ln(a)

The example is,

ln(85) = 5 ? ln(8)

Natural logarithms examples

Below are two solved problems using rules of natural logarithm -

Problem 1:

The laws of logarithms is lnsqrt(cos x ln x)

Solution:

lnsqrt(cos x ln x)

=ln(cosx ln x )^(1/2)

=(1)/(2)ln (cos x ln x)

=(1)/(2) (ln cos x ln ln x)

The factors cos x ln x are the argument of the logarithm function.

Problem 2:

Log84002=2 log8400

Solution:

= 2 log8 (20*20)

= 2 (log820 + log820)

= 2(2 log820)

Log82002= 4 log820.

Let we learn about how to do logarithms. Logarithm is just an exponent. Logarithmic of number 'x' to base 'b' is the exponent that you can put b to become the result equal to x. For example 4²= 16. Symbolically, log4(16)= 2.

If x= by, then we say that, y should be "logarithm of x to the base b or the base-b logarithm of x".

How it is represented? It is denoted as, y= logb(x).

Description:

Description of how to do logarithms:

Every exponential equation can be written also logarithmic equation and vice -versa, just by interchanging the x and y in this way.

Alternative way is to look at it is that the logbx function is well-defined as inverse of bx function.

The above statements convey that inverse relationship screening how to do an exponential equation is equivalent to logarithmic equation:

x = by is the same as y = logbx

Base b Logarithm:

Base b logarithm of x (logbx) is power to which you wish to raise b in order to get x. Symbolically,

logbx = y

means

by = x.

Notes:

1. logbx is only defined if b and x are both positive, and bis not 0 or 1
2. log10x is called the common logarithm of x and is usually written as log 10.
3. logex is called the natural logarithm of x and is sometimes written as ln x.

Examples

Example 1:

Hand calculating of logarithms.

(a) log28 =Power to which you need to raise 2 in order to get 8= 3 Since 23 = 8

(b) log41 =Power to which you need to raise 4 in order to get 1=0 Since 40 = 1

(c) log1010,000=Power to which you need to raise 10 in order to get 10,000=4 Since 104 = 10,000

(d) log101/100=Power to which you need to raise 10 in order to get 1/100=-2 Since 10-2 = 1/100

Example 2:

1000= 103 is the same as 3= log101000.

Example 3:

log381=? is the same as 3?= 81.

We can also written above definition compactly, and show how to do log as an exponent:

x=by is same as y=logb x. That is x= blog bx

Read that as “logarithmic of x in base b is exponent you put on b to get x as result.”

Learn more on about Adding 2 Digit Numbers without Regrouping and its Examples. Between, if you have problem on these topics Gaussian Elimination, Please share your comments.