The formula of quotient rule [log a (M/N) = log a M - log a N] is stated as follows: The logarithm of the quotient of two factors to any positive base other than I is equal to the difference of the logarithms of the factors to the same base.

With the help of these properties, we can express the logarithm of a product as a sum of logarithms, the log of the quotient as a difference of log and log of power as a product. Only positive real numbers have real number logarithms, …

In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 103 = 10 × 10 × 10.

The logarithm of the multiplication of x and y is the sum of logarithm of x and logarithm of y. The logarithm of the division of x and y is the difference of logarithm of x and logarithm of y. The logarithm of x raised to the power of y is y times the logarithm of x. The base b logarithm of c is 1 divided by the base c logarithm of b.

1) Product Rule: log b (m n) = log b (m) + log b (n) 2) Quotient Rule: log b (m / n) = log b (m) – log b (n) 3) Power Rule: log b (m n) = n · log b (m)

These rules apply to all logarithms, including base 10 logarithms and natural logarithms. For simplicity's sake, base ten logs are used in most of these rules: 1. b r = a is the equivalent to log b a=r (This is the definition of a logarithm.) 2. log 0 is undefined. 1. br = …

Learn the eight (8) log rules or laws to help you evaluate, expand, condense, and solve logarithmic equations. Try out the log rules practice problems for an even better understanding.

\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)

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: log(1000) = log 10 (1000) = 3

Step 1: Let [latex]{\color{red}m }= {\log _b}x[/latex] and [latex]{\color{blue}n} = {\log _b}y[/latex]. Step 2: Transform each logarithmic equation to its equivalent exponential equation. [latex]\large{m = {\log _b}x \,\,\to x\,\, = {b^m}}[/latex] [latex]\large{n = {\log _b}y \to y = {b^n}}[/latex]