Table of Contents

Welcome to **Logarithm**.app. On this site you can find everything about logarithms.

Every inverse function f ^{−1}(x) is a function that undoes another function f(x).

It essentially means that if an input x of the function f(x) produces y as output, then the input y of the inverse function f ^{−1}(x) produces the output x. And vice versa!

Logarithm are the inverse functions to exponentiations.

## Calculator

log

## Logarithm Definition

**b ^{y} = x ⇔ y = log _{b}(x) **

b, x, y ∈ R ^{+}, b ≠ 1

R ^{+} denotes the set of positive real numbers.

### Logarithm Parts

**b** is the **base**

**x** is the **argument**

**y** is the **exponent**

## Logarithm Examples

Logarithmic Form | Exponential form | |
---|---|---|

log _{2}(8) = 3 |
⇔ | 2 ^{3} = 8 |

log _{10}(1000) = 3 |
⇔ | 10 ^{3} = 1000 |

ln(x) = 1 | ⇔ | e ^{0} = 1 |

log _{3}(9) = 2 |
⇔ | 3 ^{3} = 9 |

log(100) = 2 | ⇔ | 10 ^{2} = 100 |

ln(x) is the **natural logarithm** which uses the number **e** as base. You may think of it as log _{e}(x).

The logarithm with base 2 is called **binary logarithm**, and the logarithm with base 10 is usually called **decimal logarithm**.

The decimal logarithm, which is also known as **common logarithm** and **decadic logarithm**, often has it’s base omitted:

**log _{10}(x) = log(x) **

The graph below depicts ln(x), log _{2}(x) as well as log(x) for small values of x.

## Evaluating Logarithms

1. Assumed you want to solve this equation:

log _{10}(1000000) = y.

Write it in the equivalent form:

10 ^{y} = 1000000

Take the log with base 10 from both sides:

log _{10}10 ^{y} = log _{10}(1000000)

y = 6

2. Supposed you want to solve:

log _{2}(32) = y.

Write it in the equivalent form:

2 ^{y} = 32

Take the log with base 2 from both sides:

log _{2}2 ^{y} = log _{2}(32)

y = 5

Practice makes experts, so you may soon find yourself skipping the procedure and evaluating a log just by asking, “b to what power is y”?

3. Try solving log _{4}(64) by asking yourself “4 to what power is 64?”

## Conclusion

We hope you have liked our information about the inverse function to exponentiation.

Frequently searched numbers on this site include, for example:

If you have not already done so, please **hit the share buttons**, and install our PWA app (see menu or sidebar).

If you still do things the traditional way: bookmark us now!

Thanks for your visit!