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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
