Review of Exponents and Logarithms

 

Exercises:

 

1. Rewrite as a single exponent with no fractional or negative exponents.

a) 23 x 2-4 = 23-4 = 2-1

b) 35 33 = 35-3 = 32

c) 51/2 x 52/3 = 51/2 + 2/3 = 55/6 =

d) 21/3 25/6 = 21/3-5/6 = 2-1/2 =

 

2. Evaluate:

a) log264 = 6

b) (2-2 + 3-2) 21/2 = (1/4 + 1/9) √2 = (13√2)/(72)

c) log1000 = 3

d) log255 = 1/2

e) log27 = 2.81

 

3. Write as a single log and evaluate.

a)

b)

 

4. Express as a logarithm.

a) 32 = 25 log232 = 5

b) h = 53t log5h = 3t

c) 3L = 8c-2 log83L = c-2

 

5. Use the Laws of Exponents and Logs to prove:

a) logbbt = t bt = bt

 

b)

 

6. Express as the sum or difference of logarithms. Why might this be useful for evaluating?

 

32log23 + 13log35 41log21

 

7. Solve by finding a common base.

a)

 

b)

 

c)

 

8. Solve to the nearest hundredth.

a)

 

b) 13x = 96

log1396 = x

x = 1.78

 

9. Solve to the nearest thousandth.

a)

 

b)