Introduction to natural logarithm base:
The natural logarithm of a given function is called as the logarithm to the base of e, where e is known as unreasonable constant.
e = 2.7182818.
Representation of natural logarithm base can be shown as ln(x) and loge(x).
Let us take a number x and the natural logarithm base of that number is given as the power in which e put to be raised.
eln(x) = x if x > 0
ln(ex) = x
In the natural logarithm multiplication can be formed into a addition which is shown below
ln (xy) = ln (x) + ln (y).
Natural Logarithm Base:
The base value of natural logarithm can be given as follows,
` b = n^ (1/(log_b(n)))`
The base 2 logarithm is simply denoted as lg(x) or lb(x).
The base 10 logarithm is commonly specified as log(x).
When the base is 10 the logarithm is also known as common logarithm(log10 or log).
When the base is 2 the logarithm is also known as binary logarithm(log2 or ln).
Formulae for finding natural logarithm base are as follows
logb x = loga x /loga b(change of base formula).
loge ab = loga a+ loga b(multiplication to addition formula).
loge a/b = loga a- loga b(division to subtraction formula).
logeab = b loge a(power formula).
Example Problems for Natural Logarithm Base:
Example 1:
Give the equation in exponential form for the following natural logarithm base ln 11 = 67.
Solution :
The following definition will explain you to find the equation.
If ln x = y ,then x=ey
So 11 = e67
Hence the equation can be written as e67 -11 = 0.
Example 2:
Evaluate the following natural logarithm base ln e6 without the calculator.
Solution :
we know that loge e = 1.
So ln e6 =6*1 = 6..
So the answer is6.and ln ex =x
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