**Logarithm** Aptitude Questions and Answer – Formulas & Tricks

**General Rule:** The Logarithm of any positive real number y, other than 1 when a^{x} = y, then component x is called the logarithm of y to the base a, then x = log_{a}y.

**Logarithm Properties:**

- log
_{a}(xy) = log_{a}x + log_{a}y - log
_{a}(x/y) = log_{a}x – log_{a}y - log
_{x}x = 1 - log
_{a}1 = 0 - log
_{a}(x^{n}) = n(log_{a}x) - log
_{a}x = (1/log_{x}a) - log
_{a}x = (log_{b}x / log_{b}a) = (log x / log a)

**Important Terms:**

- The logarithm of one(1) to any base is zero = Log
_{a}1 = 0 - The logarithm of zero (0) to any base greater than unity is Log
_{a}0 = -∞ - The logarithm of any number (a) to the same base is always unity, log
_{a}a = 1 - Let log
_{b}x=p, then x=b^{p}, or x=b^{log}_{b}x - The logarithm of product: Log
_{a}(m * n) = log_{a}m * log_{a}n - The logarithm of the fraction: log
_{a}(m / n) = log_{a}m – log_{a}n - Power Formula: Log
_{a}m_{n}= nlog_{a}m - Log
_{b}a = log_{c}a / log_{c}b - Log
_{b}c = 1 / log_{c}b - Log
_{b}a = log_{c}a * log_{b}c - Logx
^{n}(y^{m}) = mlog_{a}y / nlog_{a}x

**Common Logarithm**: logarithm to the base 10 are known as a common logarithm. Therefore, Log_{10}10 = 1

**Mantissa:**

Every logarithm has two parts

- Characteristics Part
- Mantissa Part

The integer part is called Characteristics Part

The decimal part of the logarithm called as Mantissa.

**Characteristics Rules:**

- To find the Characteristics of a number greater than one.
- To find the Characteristics of a number less than one.

Logarithm Aptitude Questions and Answer **With Detailed Explanation** – Quantitative Aptitude

## Logarithm

Question 1 |

If log

_{2}= 0.3010 and log_{3}= 0.4771, the value of log_{5}512 is:2.870 | |

2.967 | |

3.876 | |

3.912 |

Question 1 Explanation:

**Answer: Option C**

__Explanation:__

Question 2 |

If log27 = 1.431, then the value of log9 is:

0.934 | |

0.945 | |

0.954 | |

0.958 |

Question 2 Explanation:

**Answer: Option C**

__Explanation:__

log27 = 1.431

=> log(33) = 1.431

=> 3log

^{3}= 1.431

=> log3 = 0.477

Therefore, log9 = log(3

^{2}) = 2 log 3 = ( 2 * 0.4777)

**log9 = 0.954**

Question 3 |

If ax = by,then:

None of these |

Question 3 Explanation:

**Answer: Option C**

__Explanation:__

Question 4 |

If log

_{x}y = 100 and log_{2}x = 10, then the value of y is:2 ^{10} | |

2 ^{100} | |

2 ^{1000} | |

2 ^{10000} |

Question 4 Explanation:

**Answer: Option C**

__Explanation:__

log

_{2}x = 10 => x=2

^{10}

Therefore, log

_{x}y = 100

=> y = x

^{100}

=> y = (2

^{10}) [Put value of x]

=> y = 2

^{1000}

Question 5 |

The value of log

_{2}16 is:2 | |

4 | |

8 | |

16 |

Question 5 Explanation:

**Answer: Option B**

__Explanation:__

Let log

_{2}16 = n

Then, 2n = 16 =24

=> n =4

Therefore, log

_{2}16 = 4

Question 6 |

If log

_{10}2 = 0.3010, the value of log_{10}80 is:1.6020 | |

1.9030 | |

3.9030 | |

4.1003 |

Question 6 Explanation:

**Answer: Option B**

__Explanation:__

log

_{10}80 = log

_{10}(8 * 10)

=log

_{10}8 + log

_{10}10

=log

_{10}(23) + 1

=3log

_{10}2 + 1

=(3 * 0.3010) + 1

=1.9030.

Question 7 |

If log

_{10}5 + log_{10}(5x + 1) = log_{10}(x + 5) + 1, then x is equal to1 | |

3 | |

5 | |

10 |

Question 7 Explanation:

**Answer: Option B**

__Explanation:__

log

_{10}5 + log

_{10}(5x + 1) = log

_{10}(x + 5) + 1

=> log

_{10}5 + log

_{10}(5x + 1) = log

_{10}(x + 5) + log

_{10}10

=>log

_{10}[5 (5x + 1)] = log

_{10}[10(x + 5)]

=>5(5x + 1) = 10(x + 5)

=>5x + 1 = 2x + 10

=>3x = 9

=> x = 3.

Question 8 |

Question 8 Explanation:

**Answer: Option C**

__Explanation:__

Question 9 |

a + b = 1 | |

a - b =1 | |

a = b | |

a ^{2} - b^{2} = 1 |

Question 9 Explanation:

**Answer: Option A**

__Explanation:__

Question 10 |

Question 10 Explanation:

**Answer: Option A**

__Explanation:__

There are 10 questions to complete.