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# Important Logarithms Formulas | PDF Basic & Special Case Log Rule with Examples

## Log Formulas

Those candidates are looking for Log Formulas, they can get Important Logarithms Formulas PDF though this page.  A logarithm is the opposite of a power. In other words, if we take a logarithm of a number, we undo an exponentiation.  It is a mathematical operation which decided how many times a certain number, called the base is multiplied by itself to reach another number. Here, in this article, we are providing Basic Log Formulas and also Special Case Log Rule with Examples. If you don’t want to face any difficulty during solving the question paper, you should follow the shortcuts and easy tricks to solve the problems.

Candidates have to practice the shortcuts and formulas related to time and work daily. Along with formulas, we have given Question & answers related to Log Formulas PDF in the beneath section of this page. These solutions will help you to save your time and boost your confidence at the time of examination. So, some Important Logarithms Formulas are available on this page which is made by the team of www.recruitmentinboxx.com

### Log Formulas

Basics:

If y=logbx, then by=x:

• Where logbx=y=log to the base b of x
• Please note that b (base) is a positive real number, other than 1

If x=by, then logbx=y:

• Where logbx=y=log to the base b of x
• Please note that b(base) is a positive real number, other than 1.

Example:

• 16=24(in this expression, 4 is the power or the exponent or the index and 2 is the base)
• Hence we can say that log216=4 (i.e., log to the base 2 of 16 = 4)
• In other words, both 16=24and log216=4 are equivalent expressions

Get here all Topic Wise: Maths Formulas PDF

Common and Natural Logarithm:

• If base = 10, then we can write log x instead of log10xlog10⁡x
log x is called as the common logarithm of x
• If base =e, then we can write ln x instead of logex
ln x is called as the natural logarithm of x

Please note that e is a mathematical constant which is the base of the natural logarithm. It is known as Euler’s number. It is also called as Napier’s constant.  Logarithms – Important Properties

• logb1=0 (∵b0=1)
• logbb=1 (∵b1=b)
• y=ln x —> ey=x
• x=ey —>ln x=y
• x=ln ex=elnx
• blogbx=x
• logbby=y

Laws of Logarithms:

1. logb MN = logbM + logbN (where b, M, N are positive real numbers and b ≠ 1)
2. logb M/N=logbM−logbN (where b, M, N are positive real numbers and b ≠ 1)
3. logbMc=c logb M (where b and M are positive real numbers , b ≠ 1, c is any real number)
4. logbM=log M /logb =lnM / lnb =logkM /logkb (where b, k and M are positive real numbers, b ≠ 1, k ≠ 1)
5. logba =1/ logab (where a and b are positive real numbers, a ≠ 1, b ≠ 1)
6. If logbM=logbN then M = N (where b, M and N are positive real numbers and b ≠ 1)

Know Important Questions: Profit and Loss Formulas

Some Special Cases:

The binomials formulas

 (a + b)2 = a2 + 2ab + b2 square of the sum (a – b)2 = a2 – 2ab + b2 square of the difference a2 – b2 = (a – b)(a + b) difference of squares (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc

The trinomials formulas

 (a + b)3 = a3 + 3a2b + 3ab2 + b3 cubes of the sum (a – b)3 = a3 – 3a2b + 3ab2 – b3 cubes of the difference a3 + b3 = (a + b)(a2 – ab + b2) sum of cubes a3 – b3 = (a – b)(a2 + ab + b2) difference of cubes

The formulas for the fourth degree

• (a + b) 4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
• (a – b) 4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
• a4 – b4 = (a – b) (a + b) (a2 + b2)

Binomial theorem

• (a + b) n = an + nan – 1 b + n (n – 1)/2 an – 2 b2 + … + n! / K! (n – k)! an – k bk + … + bn
• (a – b) n = an – nan – 1 b + n (n – 1)/2 an – 2 b2 + … + (-1) k n! /k! (n – k)!an – k bk + … + (-1)nbn

Logarithm Formulas: Logarithmic Laws: Logarithm – General Questions

Ques 01: Which of the following statements is not correct?

1. log10 10 = 1
2. log (2 + 3) = log (2 x 3)
3. log10 1 = 0
4. log (1 + 2 + 3) = log 1 + log 2 + log 3 So, (2) is incorrect.

Ques 02: log√8/ log 8 is equal to:

1. 1/8
2. 1/4
3. 1/2
4. 1/8 Ques 03: If log 27 = 1.431, then the value of log 9 is:

1. 934
2. 945
3. 954
4. 958

Explanation:

log 27 = 1.431

• log (33) = 1.431
• 3 log 3 = 1.431
• log 3 = 0.477
• log 9 = log(32) = 2 log 3 = (2 x 0.477) = 0.954.

Ques 04: If log a/ b + log b/ a        = log (a + b), then:

1. a + b = 1
2. a – b = 1
3. a = b
4. a2 – b2 = 1 Ques 05: If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

1. 870
2. 967
3. 876
4. 912 Permutation and Combination Formula, Aptitude Questions, Problems and Solutions

Ques 06: If log10 2 = 0.3010, then log2 10 is equal to:

1. 699/301
2. 1000/301
3. 3010
4. 6990

Explanation:

Log2 10 = 1/ log102 = 1/ 0.3010 =10000/3010 = 1000/301

Ques 07: If log10 2 = 0.3010, the value of log10 80 is:

1. 6020
2. 9030
3. 9030
4. None of these

Explanation:

log10 80 = log10 (8 x 10)

= log10 8 + log10 10

= log10 (23) + 1

= 3 log10 2 + 1

= (3 x 0.3010) + 1

= 1.9030.

Ques 08: The value of (1/ log3 60 + 1/ log4 60 + 1/ log5 60) is:

1. 0
2. 1
3. 5
4. 60

Explanation:

Given expression = log60 3 + log60 4 + log60 5

= log60 (3 x 4 x 5)

= log60 60

= 1.

Ques 09: If log 2 = 0.30103, the number of digits in 264 is:

1. 18
2. 19
3. 20
4. 21

Explanation:

log (264)= 64 x log 2

= (64 x 0.30103)

= 19.26592

Its characteristic is 19.

Hence, then number of digits in 264 is 20.

Check Out Short Tricks: Ratio and Proportion Problems

Ques 10: The value of log2 16 is:

1. 1/8
2. 4
3. 8
4. 16

Explanation:

Let log2 16 = n.

Then, 2n = 16 = 24 –à n = 4.

Log2 16 = 4

Final words:

Dear candidates, the above information about Log Formulas is for you all. Keep practicing it daily so that you can rank well in the results. We the team of www.recruitmentinboxx.com, also wish to say all the very best.

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