1. College Algebra Notes 4.3: Laws of Logarithms
Laws of Logs: Let a be a positive number, with a≠1. Let A>0, B>0, and C be any real numbers.
loga(AB)=LogaA+LogaB
Loga(A/B)=LogaA-LogaB
Loga(AC)=ClogaA
Change of Base Formula:
Example 1: Rewrite using Laws of Logs. b. a. c.

2. College Algebra Notes 4.3: Laws of Logarithms
Laws of Logs: Let a be a positive number, with a≠1. Let A>0, B>0, and C be any real numbers.
loga(AB)=LogaA+LogaB
Loga(A/B)=LogaA-LogaB
Loga(AC)=ClogaA
Change of Base Formula:
Example 2: Evaluate c. a. b.
Example 3: Rewrite as one log a. b.

3. College Algebra Notes 4.4: Exponential and Logarithmic Equations
Guidelines for Solving Exponential Equations:
Isolate the exponential expression on one side of the equation.
Take the logarithm of each side, then use the Laws of Logarithms to “bring down the exponent.”
Solve for the variable.
Guidelines for Solving Logarithmic Equations:
Isolate the logarithmic term on one side of the equation; you may need to 1st combine the logarithmic terms.
Write the equation in exponential form (or raise the base to each side of the equation).
Solve for the variable.

4. College Algebra Notes 4.4: Exponential and Logarithmic Equations
Example 1: Find the solution to the exponential equation correct to 4dp. a. b.

5. College Algebra Notes 4.4: Exponential and Logarithmic Equations
Example 2: Solve the equation. a. b.
Not possible
Not factorable so Quadratic formula
Not possible

6. College Algebra Notes 4.4: Exponential and Logarithmic Equations
Example 3: solve the logarithmic equation for x. a. b.
Rewrite as an exponential
Rewrite as one logarithm
Rewrite as an exponential
Factor & solve
Check both to see if taking Log of a negative, if so exclude that value.
Log of a negative doesn’t work, so only
is an answer.

7. College Algebra Notes 4.4: Exponential and Logarithmic Equations
Example 4: Invest $6500 at 6% compounded daily.
a. How much money will there be after 2 years?
b. How long before there is $8000 in the account?

8. College Algebra Notes 4.4: Exponential and Logarithmic Equations
Example 5: Solve by graphing. Round to 2 dp. a. b.
So: