Chapter 4 – Exponential and Logarithmic Functions 4.5 - Exp. & Log Equations

4.5 - Exp. & Log Equations

Section 4.5 Exp. & Log Equations

Chapter 4 – Exponential and Logarithmic Functions

4.5 - Exp. & Log Equations

Solving Exponential Equations

1. Isolate the exponential expression on one side of the equation.

2. Take the logarithm of each side, then use the Laws of Logarithms to “bring down the exponent.”

3. Solve for the variable.

4.5 - Exp. & Log Equations

Examples – pg. 338Find the solution of the exponential equation,

rounded to four decimal places.5

3 1 2

13. 4 3 8

23. 2 3

1026. 2

1

x

x x

xe

4.5 - Exp. & Log Equations

Solving Logarithmic EquationsType 1

Type 1 equations are when not all terms are logarithms.

Steps:1. Isolate the logarithmic term on one side of the equation.

2. Use the Laws of Logarithms to combine the logarithmic terms.

3. Write the equation in exponential form (or raise the base to each side of the equation).

4. Solve for the variable.

5. Check your solutions in the ORIGINAL problem.

4.5 - Exp. & Log Equations

ExamplesSolve the logarithmic equations below.

3 3log (2 8) log (3 ) 2x x

ln( ) ln( 3) 7x x 7

7

3 3289.8993.00274

1 1095.633

exe

4.5 - Exp. & Log Equations

Solving Logarithmic EquationsType 2

Type 2 equations are when all terms are logarithms.

Steps:1. Use the Laws of Logarithms to combine the logarithmic terms.

2. Set the argument on the left equal to the argument on the right.

3. Solve for the variable.

4. Check your solutions in the ORIGINAL problem.

4.5 - Exp. & Log Equations

ExampleSolve the logarithmic equation below.

log(3) log(2 1) log( 2)x x

1x

4.5 - Exp. & Log Equations

ExamplesSolve the logarithmic (literal) equations below for the

specified variable of y.

ln( ) ln( ) ln( )x x C y

ln( ) 9 ln( )y x C

x Cy

x

9xy Ce

4.5 - Exp. & Log Equations

More Examples – pg. 338

Solve the logarithmic equation for x.

9 9

43. 4 log 3 3

46. 2 log log 2 log 3 4

53. log 5 log 3 1

x

x x

x x