Quants Menu

- HCF and LCM
- Number System
- Number Decimals & Fractions
- Surds and Indices
- Divisibility
- Ages
- LCM
- HCF
- Inverse
- Speed Time and Distance
- Work and Time
- Boats and Streams
- Pipes and Cisterns
- Averages
- Allegations and Mixtures
- Ratio and Proportions
- Simple & Compound Interest
- Simple Interest
- Compound Interest
- Percentages
- Profit & Loss
- Successive Discount 1
- Successive Discount 2
- AP GP HP
- Arithmetic Progressions
- Geometric Progressions
- Harmonic Progressions
- Probability
- Permutation & Combination
- Combination
- Circular Permutation
- Geometry
- Heights and Distances
- Perimeter Area and Volume
- Coordinate Geometry
- Venn Diagrams
- Set Theory
- Algebra
- Linear Equations
- Quadratic Equations
- Logarithms
- Clocks
- Calendars
- Clocks and Calendars
- Finding remainder of large powers

PREPINSTA PRIME

# Logarithms Questions and Answers

**Logarithms ****Questions and Answers**

**Logarithm Questions and Answers**

**Common Logarithm and Natural Logarithm: **

- Common logarithm has base 10 ($b = 10$) and is denoted as $\log(x)$, while natural logarithm has base $e$ (Euler’s number) and is denoted as $\ln(x)$.

**Logarithm Rules:**

- Product Rule: log_{b}\left ( xy \right )= log_{b}\left ( x \right )+log_{b}\left ( y \right )
- Quotient Rule: log_{b}\left ( \frac{x}{y} \right )=log_{b}\left ( x \right )-log_{b}\left ( y \right )
- Power Rule: log_{b}\left ( x \right )^{n}=nlog_{b}\left ( x \right )

**A logarithm denote as the contradictory of power. In other terms, if we go for a logarithm of a particular value, we unknot exponentiation. Logarithm Questions and Answers are discussed below:**

For instance: If the base is taken as b = 3 and increase it to the power of k = 2 we get the result as 32. The result is referred as c, showed by 32 = C. The rules of exponentiation can be used to evaluate that the result is C =32 = 8.

Given an example, consider that someone inquired “2, raised to which power is equivalent to 16”? The result will be 4. It is further articulated by the logarithmic calculation, i.e. log2 (16) = 4, which is further spoken as “log base two of sixteen is four.”

**Logarithm form**

- Log
_{2}(8) = 3 - Log
_{4}(64) = 3 - Log
_{5}(25) = 2

**Exponential form**

- 2^3= 8
- 4^3= 64
- 5^2= 25

Generalizing the examples above leads us to the formal definition of a logarithm.

Logb (a) =c ↔ bc =a

Both the equations define the similar link where:

‘b’ is considered as the base,

c is considered as the exponent

a is considered as the argument

### Prime Course Trailer

### Related Banners

Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription

## Also Check Out

**Logarithm Questions and Answers**

Please login to report

**Also Check Out**

**Get over 200+ course One Subscription**

Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others

- Clocks – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Calendars – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Clocks and Calendars – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts

**Others**

- Clocks –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Calendars –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Clocks and Calendars –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts

**Others**