Comprehensive guide to the rules of logarithmic and exponential functions with worked examples, step-by-step solutions, and practice questions for students.
Log rules are rules that are used to operate logarithms. Since logarithm is just the other way of writing an exponent, we use the rules of exponents to derive the logarithm rules. There are mainly 4 important log rules which are stated as follows:
This page covers all 8 log rules (including the change of base formula and log exponent rules). Each log rule is covered in-depth with simple explanations and examples.
Logarithm rules mirror these laws — the log of a product becomes a sum, the log of a quotient becomes a difference, and the log of a power brings the exponent out front.
In other words, logarithms are exponents. Remarks: log x always refers to log base 10, i.e., log x = log10x . ln x is called the natural logarithm and is used to represent logex , where the irrational number e 2 : 71828. Therefore, ln x = y if and only if ey= x .
The following rules hold for any log c(x), c > 0, but are presented using the natural log function loge(x) = ln(x), as we will use this most often. Let a and b be real numbers.
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 Rules - Narural Log Rules (Rules of Ln) | Logarithm Rules - Cuemath
The base b logarithm of a number is the exponent that we need to raise the base in order to get the number. 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.