# Log and Antilog Calculator

Use this expanding logarithms calculator to calculate your log and antilog problems. Enter the number and select the base value in the logarithmic functions calculator. Press the Calculate button to get the result of your entered values.

## Log and Antilog

The logarithmic calculator is an antilog calculator as well as a log base calculator** **because it calculates both log and antilog in one place.

In this space, we will discuss log definition, antilog definition, rules and formula of log, how to find log without logarithm solver, and how to find antilog without inverse log calculator. Keep reading if you are a math geek or just interested in this topic.

## What is log?

**“**In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number ** x** is the exponent to which another fixed number, the

*base*

**, must be raised, to produce that number**

*b*

*x***.**

**”**

Logs are ways of expressing a number, it has a base number raised to a power. Logs and antilogs are important components of mathematics and are used in mathematical equations often.

## What is antilog?

As the name suggests, antilog is the reverse function of the log. It is used to remove the applied log from a function. Antilog inverses the result of a logarithm function.

## Log formula and rules

The formula for log is:

Where ** b **represents the logarithmic base.

The antilog equation can be expressed as:

Here are some of the log rules which are used frequently.

### Product

*ln**(**xy**) = **ln**(**x**) + **ln**(**y**)*

### Quotient

*ln**(**x**/**y**)*** = ***ln**(**x**) − **ln**(**y**)*

Log of power

*ln(x ^{y}) = yln(x)*

### Log of exponent

*ln**(**e**) = **1*

### Log of one

*ln**(**1**) = **0*

### Log of reciprocal

*ln**(**1**/**x**) = −**ln**(**x**)*

Where, ** ln **represents the

**natural log.**

## How to calculate log?

Logs can be calculated using the logarithm calculator. Below, we will discuss the manual method to find the log using the logarithm rules.

### Example:

Find the ** log of 256** with

*base 2.***Solution:**

**Step 1: **Write down and identify the values.

**x = 256**

**b = 2**

**Step 2: **Place the values in the standard log equation.

**Step 3: **Raise ** y **as the power of the base

**and remove the**

*b***log.**

**2 ^{y} = 256**

**2 ^{y} = 2^{8}**

**2 **is the coefficient on both sides, so they will cancel each other and we will get the value of *y.*

**y = 8**

## How to calculate antilog?

Want to learn how to find antilog before using an antilog calculator online?** **Follow the steps below to calculate antilog with an example.

### Example:

Find the ** antilog of 2.5** with

*base 6.***Solution:**

**Step 1: **Write down and identify the values.

**x = 2.5**

**b = 6**

**Step 2: **Use the antilog equation and place the values.

**y = 88.18**

## Some important antilog values

antilog(2) | 10^{2} | 100 |

antilog(1) | 10^{1} | 10 |

antilog(10) | 10^{10} | 10000000000 |

antilog_{2} 5 | 2^{5} | 32 |

antilog_{2} 2 | 2^{2} | 4 |

antilog(3) | 10^{3} | 1000 |

antilog_{3} 5.5 | 3^{5.5} | 420.8883 |

antilog_{2} 1.5 | 2^{1.5} | 2.8284 |

antilog(15.6) | 10^{15.6} | 3.981071705535E+15 |

antilog(8) | 10^{8} | 100000000 |

antilog(0) | 10^{0} | 1 |

antilog(4) | 10^{4} | 10000 |

antilog(5) | 10^{5} | 100000 |

antilog(9) | 10^{9} | 1000000000 |

antilog(12) | 10^{12} | 1000000000000 |

antilog(20) | 10^{20} | 1.0E+20 |

antilog(22) | 10^{22} | 1.0E+22 |

antilog(13) | 10^{13} | 10000000000000 |

antilog(18) | 10^{18} | 1.0E+18 |

antilog(5) | 10^{5} | 100000 |

antilog(14) | 10^{14} | 1.0E+14 |

## Logarithm Table

Table of base 10, base 2 and base e (ln) logarithms:

x | log_{10 }x | log_{2 }x | log_{e }x |
---|---|---|---|

0 | undefined | undefined | undefined |

0^{+} | - ∞ | - ∞ | - ∞ |

0.0001 | -4 | -13.287712 | -9.210340 |

0.001 | -3 | -9.965784 | -6.907755 |

0.01 | -2 | -6.643856 | -4.605170 |

0.1 | -1 | -3.321928 | -2.302585 |

1 | 0 | 0 | 0 |

2 | 0.301030 | 1 | 0.693147 |

3 | 0.477121 | 1.584963 | 1.098612 |

4 | 0.602060 | 2 | 1.386294 |

5 | 0.698970 | 2.321928 | 1.609438 |

6 | 0.778151 | 2.584963 | 1.791759 |

7 | 0.845098 | 2.807355 | 1.945910 |

8 | 0.903090 | 3 | 2.079442 |

9 | 0.954243 | 3.169925 | 2.197225 |

10 | 1 | 3.321928 | 2.302585 |

20 | 1.301030 | 4.321928 | 2.995732 |

30 | 1.477121 | 4.906891 | 3.401197 |

40 | 1.602060 | 5.321928 | 3.688879 |

50 | 1.698970 | 5.643856 | 3.912023 |

60 | 1.778151 | 5.906991 | 4.094345 |

70 | 1.845098 | 6.129283 | 4.248495 |

80 | 1.903090 | 6.321928 | 4.382027 |

90 | 1.954243 | 6.491853 | 4.499810 |

100 | 2 | 6.643856 | 4.605170 |

200 | 2.301030 | 7.643856 | 5.298317 |

300 | 2.477121 | 8.228819 | 5.703782 |

400 | 2.602060 | 8.643856 | 5.991465 |

500 | 2.698970 | 8.965784 | 6.214608 |

600 | 2.778151 | 9.228819 | 6.396930 |

700 | 2.845098 | 9.451211 | 6.551080 |

800 | 2.903090 | 9.643856 | 6.684612 |

900 | 2.954243 | 9.813781 | 6.802395 |

1000 | 3 | 9.965784 | 6.907755 |

10000 | 4 | 13.287712 | 9.210340 |

### References:

- How to Calculate Antilog? by sciencing.com
- Review of logarithms and antilogarithms - FAQ 1447 - graphpad.com