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Algebra 2B
Properties of Logarithms HW – No Calculator
Name ___________________________
Condense each logarithmic expression to a single logarithm with no coefficients. If your answer can be
simplified without a calculator, evaluate it.
1) log6 9  log6 4
2) log8 2  log8 32
3) log3 5  log3 6
4) log 2 56  log 2 7
5) log x  log 3
6) log9 5  log9 y  log9 4
7) 3log 2 x
8) 2log12 6  log12 4
9) 12 log 2 81  log 2 15
10) 3logb m  2logb n
11) 2logb x  3logb y
12) 2logb x  3logb y  5logb z
Write as a sum or difference of logarithms with no exponents (Expand).
13) log5 (3i2)
14) log  17 
16) log 2  x3 y 7 
17) log3  x 5 
 19 
A little review:
19) Rewrite in logarithmic form: 25  32

4

y 
15) log 7 æç 5i3ö÷
è 2 ø
18) log3  x 8y 
 z 
4
3
20) Rewrite in exponential form log3 81  4
Solve the equation by changing from log form to exponential form or vice versa.
21) 3x  50
22) log3 x = 4
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