Sep 17, 2024 · Solved Examples on Exponential and Logarithmic Functions. Example 1: Solve the equation log 3 (x) + log 3 (x-2) = 1. Solution: Combine the logarithms: log 3 (x(x - 2)) = 1. Convert to exponential form: x(x - 2) = 3 1 = 3. Factor the quadratic equation: (x - 3)(x + 1) = 0. The solutions are x = 3 and x = -1. However, x must be positive, so x = 3.

May 1, 2021 · In this section, we will discuss logarithmic functions and exponential functions. The exponent rules we learned last section also apply to the exponents we see in exponential functions, so here we will focus on the relationship between exponential and logarithmic functions.

Always try to use Natural Logarithms and the Natural Exponential Function whenever possible. The Common Logarithm. When the base is 10 we get: The Common Logarithm log 10 (x), which is sometimes written as log(x) Engineers love to use it, but it is not used much in mathematics.

Explain the relationship between exponential and logarithmic functions. Describe how to calculate a logarithm to a different base. Identify the hyperbolic functions, their graphs, and basic identities. In this section we examine exponential and logarithmic functions.

What are Exponential and Logarithmic Functions? Exponential Function Definition: An exponential function is a Mathematical function in the form y = f (x) = b x, where “x” is a variable and “b” is a constant which is called the base of the function such that b > 1.

Examples, solutions, videos, worksheets, and activities to help PreCalculus students learn about exponential and logarithmic functions. The following diagram gives the definition of a logarithmic function.

EXPONENTIAL EQUATIONS The properties given above are useful in solving equations, as shown by the next examples. Example 1. USING A PROPERTY OF EXPONENTS TO SOLVE AN EQUATION. Solve (13)x=81. First, write 13 as 3− 1, so that (13)x=3− x. Since 81=34,

Sample Exponential and Logarithm Problems 1 Exponential Problems Example 1.1 Solve 1 6 3x 2 = 36x+1. Solution: Note that 1 6 = 6 1 and 36 = 62. Therefore the equation can be written (6 1) 3x 2 = (62)x+1 Using the power of a power property of exponential functions, we can multiply the exponents: 63x+2 = 62x+2 But we know the exponential function ...

Unit 7: Exponential and Logarithmic Functions . Unit 7 Learning Outcomes 7.1: Introduction to Exponential Functions ... Example 8 Solving Exponential Functions in Quadratic Form. Solve . Solution. Get one side of the equation equal to zero. Factor by the FOIL method. If a product is zero, then one factor must be zero. ...

Exponential and logarithmic functions: The function defined by f (x) = bx; (b>0), b≠1) is called an exponential function with base b and exponent x.