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Rules For Natural Logarithms

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.
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