Rules of Logarithm and Exponential - Questions with Solutions
The rules of logarithmic and exponential functions and the properties of these functions are presented. The use of these rules to simplify expressions and solve equations are explained through examples and questions with detailed solutions.
Rules of the Logarithmic functionsFor U and V real positive numbers, b positive and not equal to 1:
Example 1
Rules of the Exponential functionsFor \(x\) and \( y\) real numbers and \( a \) real and positive:
Example 2
Inverse Rule - Relationship Between the Logarithmic and Exponential FunctionsThe exponential and logarithmic functions are inverses of each other. Hence \[ \log_b x = y \iff x = b^y \] Notesa - The bases of the logarithmic and exponential functions are the same. b - \( y \) is the exponent in the exponential form which means \( \log_b x \) is the exponent the base \( b \) must be raised to obtain \( x \).
Example 3
Example 4
Example 5
Example 6
Questions with SolutionsPart 1
Part 2
Solutions to the Above Questions Part 1
Part 2
More References and Links to logarithmic FunctionsLogarithmic Functions (interactive tutorial).Solve Logarithmic Equations - Detailed Solutions How Solve Exponential Equations Questions with Detailed Solutions Graph Logarithmic Functions. Tutorial on Exponential and Logarithmic Equations. Graph of Logarithmic and Exponential Functions - Self Test. Solve Exponential and Logarithmic Equations (self test). |