In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes. Trivial mathematical identities are relatively simple (for an experienced mathematician), though not necessarily unimportant. The trivial logarithmic identities are as follows:

One of the most common ways to manipulate an expression with a logarithm is to convert a product inside a logarithm into a sum of logarithms or vice-versa. This is done with the following identity: A proof of this identity will be shown. Now, the left-hand side is more difficult to simplify.

2012年9月20日 · Let $\gcd(a,b) = 1$ and $x = a^nb$ where $a,b,n \in \mathbb{Z}$, then $$\begin{aligned} \log_a x &= n + \frac{\ln b}{\ln a} = n + \frac{\ln b}{\ln(b+1)}\frac{\ln(b+1)}{\ln(b+2)}\cdots \frac{\ln(b+(m-1))}{\ln(b+m)}\frac{\ln (b+m)}{\ln a} \newline &= n + \log_{b+1} b\log_{b+2}{b+1}\cdots \log_{b+m} (b + (m-1)) \ln_{a} (b+m). \end{aligned}$$

Login Contents of this Precalculus episode: Logarithmic Functions, Logarithmic equations, Exponential identities, Logarithmic identities, solve the exponential equations, Solve the logarithmic equations.

log(100) This usually means that the base is really 10. It is called a "common logarithm". Engineers love to use it. On a calculator it is the "log" button. It is how many times we need to use 10 in a multiplication, to get our desired number.

Example 1: Solve log 2 (x) + log 2 (x – 2) = 3 Solution : Here we need to use logarithmic identities to combine the two terms on the left-hand side of the equation: log 2 (x) + log 2 (x – 2) = 3

\log_{\msquare} \sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div: x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} \frac{\partial}{\partial x} \int \int_{\msquare}^{\msquare} \lim \sum \infty \theta (f\:\circ\:g) f(x)

Wikipedia says: The numerical value for logarithm to the base $10$ can be calculated with the following identity: $$\mathrm {log_ {10}} (x) = \frac {\mathrm {ln} (x)} {\mathrm {ln} (10)} \\ \text {or...

Logarithm of quotient of two numbers is equal to difference of their logs. log b (m n) = log b m – log b n. The rules of logarithms which simplify the way to find the values of logarithmic terms by expressing quantity and base quantity of log terms in exponential form. (1). log b m n = n log b m. (2). log b y m = (1 y) log b m.

A logarithm (to base b) of a number x is the exponent y that satisfies x = by. It is written log b (x) or, if the base is implicit, as log (x). Mathematically, expressed as: Natural logarithm (log e (x), ln (x), log (x), or Ln (x)) where e » 2.71828...