1. Solving Logarithmic Equations

2. Solving an Exponential Equation
Ex. 73x=20
log720=3x
1.5395≈3x
x≈.5132
Write in log form
Evaluate in the calculator
Divide both sides by 3.

3. Solving an Exponential Equation
Ex. 3x+4=101
log3101=x+4
4.2=x+4
0.2=x

4. Try these. Solve for x. Ex. 2x=3 Ex. 4x=19 Ex. 5-3x=-40 Ex. 14x+1=36

5. log b Change of Base Formula logbM=logM Ex. log315 Ex. log5400

6. Solving a Logarithmic Equation
Ex. log(3x+1)=5 Ex. log(7-2x)=-1
105=3x+1
100,000=3x+1
99,999=3x
33,333=x
10-1=7-2x
0.1=7-2x
-6.9=-2x
3.45=x

7. Solve for x.
Ex. log 2x = -1
Ex. log (3x+1) = 2
Ex. log (5-2x) = 0
Ex. 3 log x = 1.5
x=.05
x=33
x=2
x=3.162

8. Using Logarithmic Properties to Solve an Equation
Ex. 2logx-log3=2 Ex. log6-log3x=-2
log 6 = -2 3x
10-2 = 6
.01 = 6
.03x=6
x=200
logx2-log 3 = 2
log x2 =2 3
102=x2
100=x2
300=x2
x=17.32 or x=-17.32