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.

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.

Exponents and Logarithms work well together because they "undo" each other (so long as the base "a" is the same): They are "Inverse Functions" Doing one, then the other, gets us back to where we started: Doing ax then loga gives us back x: loga(ax) = x. Doing loga then ax gives us back x: aloga(x) = x.

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.

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.

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,

Apr 20, 2025 · For example, \[\log_2(8)=3\nonumber \] since \(2^3=8\), \[\log_{10}\left(\dfrac{1}{100}\right)=−2 \nonumber \] ... However, exponential functions and logarithm functions can be expressed in terms of any desired base \(b\). If you need to use a calculator to evaluate an expression with a different base, you can apply the change-of-base ...

Jun 6, 2018 · Exponential Functions – In this section we will introduce exponential functions. We will give some of the basic properties and graphs of exponential functions. We will also discuss what many people consider to be the exponential function, f (x) =ex f (x) = e x. Logarithm Functions – In this section we will introduce logarithm functions.

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.

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 ...