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Day 11
Notes
6.11 Notes – Change of base
and log equations
Objectives:
1) Use common logs to solve equations.
2) Apply the change of base formula.
Solve Logarithm equations by applying log properties:
2
log 7 8
3
1) 2log3 x  log3 9
2) log7 x 
3) 2log6 x  log6 4  log6 64
4) log8 48  log8 y  log8 4
5) log3 x  5log3 2  log3 8
6) log 2(3u  14)  log 2 5  log 2 2u
7) ln( x  3)  ln x  ln 4
8) ln 4  ln x  ln e2
9) 3log5( x 2  9)  6  log5 1
Change of base formula:
Why would we ever want to change the base of our logarithm? Well, the reason is that we
cannot evaluate a logarithm like _________________ in our heads.
Change of Base Formula:
log a c 
Examples:
1) log 4 25 
2) log3 18 
3) log6 5 
Use logs to solve exponential equations:
State your answer as an exact answer and then approximate your answer to the nearest thousandths.
1) 3x  27
2) 5x  120
3) e x  52
4) 4 2 x  27
5) 2x 4  82
6) e 2 x 3  42
x3
7) 5  72
3
8) 4  e  10
x