## 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

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

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