# Value of Log 2

**The value of log 2, to the base 10, is 0.301. **The log function or logarithm function is used in most mathematical problems that hold the exponential functions. Log functions are used to eliminate the exponential functions when the equation includes exponential values.

The logarithmic function is defined by:

** if log _{a}b = x, then a^{x} = b.**

Where,

x is the logarithm of a number ‘b.’

‘a’ is the base of the log function.

**Note:** The variable “a” should be any positive integer, and it should not be equal to 1.

The classification of logarithmic functions is:

- Common Logarithmic Function – Log function with base 10
- Natural Logarithmic Function – Log function with base e

If the base of the logarithmic function is other than 10 or e, convert it into either base e or base 10 using the change of base rule. In this article, we are going to discuss the value of log 2 to the base 10 and base e with a step-by-step procedure also learn the log values from 1 to 10.

## How to calculate the value of Log 2?

Now, let us discuss how to find the value of log 2 using a common log function and natural log function.

### Value of Log_{10} 2

The log function of 2 to the base 10 is denoted by “log_{10} 2”.

According to the definition of the logarithmic function,

Base, a = 10 and 10^{x} = b

With the use of logarithm table, the value of log 2 to the base 10 is given by 0.3010.

** Log _{10} 2 = 0.3010**

### Value of ln (2) or log_{e} 2

The natural log function of 2 is denoted by “log_{e} 2”. It is also known as the log function of 2 to the base e. The representation of the natural log of 2 is ln(2).

The value of log_{e }2 is equal to 0.693147.

** log _{e }2 = ln (2) = 0.693147**

## Log Values from 1 to 10

The values from log 1 to 10 to the base 10 are:

Log 1 | 0 |

Log 2 | 0.3010 |

Log 3 | 0.4771 |

Log 4 | 0.6020 |

Log 5 | 0.6989 |

Log 6 | 0.7781 |

Log 7 | 0.8450 |

Log 8 | 0.9030 |

Log 9 | 0.9542 |

Log 10 | 1 |

## Ln Values from 1 to 10

The values from log 1 to 10 to the base e are:

ln (1) | 0 |

ln (2) | 0.693147 |

ln (3) | 1.098612 |

ln (4) | 1.386294 |

ln (5) | 1.609438 |

ln (6) | 1.791759 |

ln (7) | 1.94591 |

ln (8) | 2.079442 |

ln (9) | 2.197225 |

ln (10) | 2.302585 |

### Solved Problem

**Question :**

Solve log (x-2) – log (2x -3) = log 2

**Solution:**

Given that, log (x-2) – log (2x -3) = log 2

Using the properties of the logarithm (log a – log b = log a/b)

It can be written as,

log ((x-2)/(2x-3)) = log 2

Since the base of the log function is 10, it becomes;

⇒10^{log((x-2)/(2x-3))} = 10^{log(2)}

⇒(x-2)/(2x-3) = 2

Bring 2x-3 to R.H.S

⇒(x-2)= 2(2x-3)

⇒x-2=4x-6

⇒x-4x =-6+2

⇒-3x = -4

⇒ x = 4/3

Therefore, the value of x is 4/3.

To learn the values of natural log and common log, register with BYU’S – The Learning App and also watch interactive videos to clarify the doubts.