6.3A – Logarithms and Logarithmic Functions

6.3A – Logarithms and Logarithmic Functions Objective: TSW evaluate logarithmic expressions.

Definition of a Logarithmic Function For x > 0 and b > 0, y = logbx is equivalent to by = x. So, a logarithm allows us to solve for unknown exponents since a logarithm is an exponential equation  Logarithmic form: y = logbx Exponential Form: by = x.

Examples…. 1. Write each equation in its equivalent exponential form. a. 2 = log5x b. 3 = logb 64 c. log3 7 = y We will use the fact that: y = logbx means by = x,

Examples… • Write each equation in it’s equivalent logarithmic form. a. 2r = 10 b. 17= b3.2 c. 122 = 144

Now Let’s Apply the Definition to Solve. Here are the steps: • Set the logarithm equal to y • Rewrite the logarithm in exponential form • Break the bases down so they are the same!!! • REMEMBER, if the bases are equal, the exponents MUST BE equal! • Set the exponents equal and solve for y. • CHECK YOUR SOLUTION! Logarithmic form: y = logbx Exponential Form: by = x.

Let’s Try a Few… 3. Evaluate a. log2 16 b. log3 9

Evaluate a. log5(1/25) b. log25 5

Homework! Pg. 496 #’s 1-7(all), 13-23(odds), 25-36(all).

6.3A – Logarithms and Logarithmic Functions