Logarithm Formula
Logarithm is very interesting chapter in maths because it is
easy to solve the questions using certain formulas. The Logarithm (log)
comes in quantitative
aptitude section. This chapter can give at least 2-3 marks in the exam easily. Most
of all candidates thought that Logarithm questions are boring and lengthened but
it is not like that. If deserving and ambitious students have queries connected
with log topic then do not worries and have patience because the team members
of ejobhub will give most possible tricks to solve your query and also will
make this topic engrossed for you all.
To make Logarithm topic easy and make good combination with
the questions then read this article and learn all the Logarithm formulas and
important log shortcut tricks to crack competitive exam with better marks. To find
the path more clearly, initially solve the questions in detail using maximum
formulas. Just the once you get advanced with the mechanisms of this
deceptions, you will find it immensely supportive. Shortcut Tricks will help
you to beat the entire question Exam and get answers in just few seconds. More
details in favor of Logarithm Formula are given below for all the appliers who
are looking to present in exam. All the best!!
Definition Of
Logarithm: Definition of Logarithm in math- It is the power to which a
foundation should be raised to capitulate a given number. Expressed
mathematically, just suppose-
Basic Properties of Logarithms: Logarithms
were rapidly adopted by scientists because of diverse functional properties
that simplify extensive, monotonous calculations. For instance, scientists
could find the artifact of two numbers x and y by looking
up every number’s logarithm in a particular table. Here we have indicated
the Logarithms Properties which are considers as fundamental properties, so
have a look here!!!!
loga (xy)
|
loga x + loga y
|
logb(x/y)
|
log b (x)- log b (y)
|
loga (xn)
|
n(loga x)
|
logb (xp)
|
p logb(x)
|
logb (x)
|
loga(x)/loga(b)
|
logx x
|
1
|
loga 1
|
0
|
Common Logarithms:
Logarithms to the base 10 are known as common logarithms. The logarithm of a
number contains two parts, namely 'characteristic' and 'mantissa'.
Basic rules for logarithms: See this table-
Special
Cases
|
Formula
|
Product
|
ln(xy)=ln(x)+ln(y)ln(xy)=ln(x)+ln(y)
|
Quotient
|
ln(x/y)=ln(x)−ln(y)ln(x/y)=ln(x)−ln(y)
|
Log of power
|
ln(xy)=yln(x)ln(xy)=yln(x)
|
Log of ee
|
ln(e)=1ln(e)=1
|
Log of one
|
ln(1)=0ln(1)=0
|
Log reciprocal
|
ln(1/x)=−ln(x)
|
EXPONENTIAL GROWTH FORMULA:
P(t)=P0ert
Where:
t = time (number of periods)
P(t) = the amount of some quantity at time t
P0P0 = initial amount at time t = 0
r = the growth rate
MARGIN OF ERROR FORMULA:
E=Z(Ɑ/2)(Ɑ/√n)
Z(Ɑ/2) = represents the critical value.
Z(Ɑ/√n) = represents the standard deviation
PERCENTILE FORMULA:
Percentile = Number
of Values Below / TotalNumberofValues×100
Read Also: जानिये Reasoning के लिए कैसे तैयारी करे
Logarithm
Characteristics: The internal part of the logarithm of a number is
called its characteristic.
Case I: When the number is greater than 1.
In this case, the characteristic is one less than the number
of digits in the left of the decimal point in the given number.
Case II: When the number is less than 1.
In this case, the characteristic is one more than the number
of zeros between the decimal point and the first significant digit of the
number and it is negative.
Instead of -1, -2 etc. we write 1 (one bar), 2 (two bar),
etc.
Examples:
Number
|
Characteristic
|
Number
|
Characteristic
|
654.24
|
2
|
0.6453
|
1
|
26.649
|
1
|
0.06134
|
2
|
8.3547
|
0
|
0.00123
|
3
|
Shortcut Tricks to
Crack Competitive Exam: Check all the questions for more details-
Question: If log 2 = 0.3010 and log 3 = 0.4771, the
value of log5 512 is:
A. 2.870
B. 2.967
C. 3.876
D. 3.912
Answer: C
Question: Solve
log2(x) + log2(x – 2) = 3
Solution:
log2(x) + log2(x – 2) = 3
log2 [(x)(x – 2)] = 3
log2(x2 – 2x) = 3
log2(x2 – 2x) = 3
23 = x2 – 2x
8 = x2 – 2x
0 = x2 – 2x – 8
0 = (x – 4)(x + 2)
x = 4, –2
x = 4
Question: Solve
log2(x2) = (log2(x))2
Solution:
log2(x2) = [log2(x)]2
log2(x2) = [log2(x)] [log2(x)]
2·log2(x) = [log2(x)] [log2(x)]
0 = [log2(x)] [log2(x)] – 2·log2(x)
0 = [log2(x)] [log2(x) – 2]
log2(x) = 0 or log2(x) – 2 = 0
20 = x or log2(x) = 2
1 = x or 22 = x
1 = x or 4 = x
x = 1, 4
Reminder: Dear
candidates now follow the given tips and tricks for log questions solving soon.
Take a Look on Below Table
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