1. Do Now: Determine the value of x in the expression.
1. 2x  x 
4. 4x  x  x 

2. 6.3 Logarithms and logarithmic functions
Algebra II
6.3 Logarithms and
logarithmic functions

3. Logarithms
We know that 22 = 4 and 23 = 8. What value of x does 2x = 6? Mathematicians define this x-value using a logarithm and write x = log26.

4. Definition of Logarithm with base b
Let b and y be positive real numbers with b ≠ 1. The logarithm of y with base b is denoted by logby and is defined as:
The expression logby is read as “log base b of y”

5. What’s important?
This definition tells us that the following equations are equivalent. The first is logarithmic form, and the second is exponential form.

6. Rewrite the logarithmic equation in exponential form.

7. Important
Numbers 1 and 2 in the last example illustrate two special logarithm values that we should learn to recognize before we start graphing.

8. Rewrite the exponential equation in log notation.

9. Evaluate the logarithm.

10. Common Logarithm and Natural Logarithm

11. Evaluating Common and Natural Log
Evaluate using a calculator. Round your answer to three decimal places
(a) log (b) ln 0.3

12. Evaluate logs using a calculator.