# How do you prove logarithmic powers?

**Logarithm Properties**

- Product
**Rule**. The**logarithm**of a product is the sum of the**logarithms**of the factors. log_{a}xy = log_{a}x + log_{a}y. **Quotient Rule**. The**logarithm**of a**quotient**is the**logarithm**of the numerator minus the**logarithm**of the denominator log_{a}= log_{a}x - log_{a}y.- Power
**Rule**log_{a}x^{n}= nlog_{a}x. - Change of Base
**Rule**.

Likewise, people ask, what is the error in the proof?

The **error in the proof** is the assumption in the diagram that the point O is inside the triangle.

One may also ask, what is LN equal to? The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately **equal to** 2.718281828459. The natural logarithm of x is generally written as **ln** x, log_{e} x, or sometimes, if the base e is implicit, simply log x.

Correspondingly, what are the log rules?

Logarithm rules

Rule name | Rule |
---|---|

Logarithm product rule | log_{b}(x ∙ y) = log_{b}(x) + log_{b}(y) |

Logarithm quotient rule | log_{b}(x / y) = log_{b}(x) - log_{b}(y) |

Logarithm power rule | log_{b}(x ^{y}) = y ∙ log_{b}(x) |

Logarithm base switch rule | log_{b}(c) = 1 / log_{c}(b) |

What is log of a number?

A logarithm is the power to which a **number** must be raised in order to get some other **number** (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: **log** 100 = 2. because.