 ## Logarithm

The Logarithm topic is very important in quantitative aptitude section. At least 2-3 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 Want TO Know?? How To Improve your IQ

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

 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

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 log5 512 is:

1. 2.870
2. 2.967
3. 3.876
4. 3.912 Question: If log 2 = 0.30103, the number of digits in 264 is:

1.   18
2.   19
3.   20
4.   21 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