6.3A – Logarithms and
Logarithmic Functions
Objective: TSW evaluate
logarithmic expressions.
Definition of a Logarithmic Function
For x > 0 and b > 0,
Logarithmic
Exponential
y = form:
logb xy =islog
equivalent
to by = Form:
x. by = x.
bx
So, a logarithm allows us to solve for
unknown exponents since a logarithm is
an exponential equation 
Examples….
1. Write each equation in its equivalent
exponential form.
a. 2 = log5 x
b. 3 = logb 64 c. log3 7 = y
We will use the fact that: y = logb x means by = x,
Examples…
2. 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:
1. Set the logarithm equal to y
2. Rewrite the logarithm in exponential form
Logarithmic form: y = logb x
Exponential Form: by = x.
3. Break the bases down so they are the same!!!
4. REMEMBER, if the bases are equal, the exponents
MUST BE equal!
5. Set the exponents equal and solve for y.
6. CHECK YOUR SOLUTION!
Let’s Try a Few…
3. Evaluate
a. log2 16
b. log3 9
4. Evaluate
a. log5(1/25)
b. log25 5
Homework!
Pg. 496 #’s 1-7(all), 13-23(odds), 25-36(all).