Logarithm Formula, Log Shortcut Tricks to Crack Competitive Exam Questions
Logarithm
The Logarithm topic is very
important in quantitative aptitude section. At least 23 marks will cover this
topic in the exam. Most of the students think that Logarithm topic is tedious
and protracted topic but it is not like that. If students have queries
regarding this topic then do not worry, we will try to solve your query and also
will make this topic engrossed for you all. Well, so as to make Logarithm topic
easy, in this article we are providing you Logarithm formulas and important log
shortcut tricks to crack competitive exam.
To comprehend the way more
clearly, initially solve the questions in detail. Just the once you get advanced
with the mechanisms of this deceptions, you will find it immensely supportive. Shortcut
Tricks will help you to Crack Competitive Exam and get answers in just few
seconds. In below section we are providing you some important questions of Logarithm
chapter, by solving these questions you will get to know the Formulas and shortcut
tricks, which will save your time. We hope that this will be helpful for your
exams. Please have a look and stay in link with www.privatejobshub.in.
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'.
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Basic rules for
logarithms
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
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
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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

Log Shortcut Tricks
Question: If
log 2 = 0.3010 and log 3 = 0.4771, the value of log_{5} 512 is:
1. 2.870
2. 2.967
3. 3.876
4. 3.912
Answer: Option 3
Question: If
log 2 = 0.30103, the number of digits in 264 is:
1.
18
2. 19
3. 20
4. 21
Answer: Option 3
Question:
Question:
Question:
Explanation:
Question:
Question:
Solve log2(x) +
log2(x – 2) = 3
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
Take
a Test Now

Question:
Solve log2(x2) =
(log2(x))2
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
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