Logs & Exponentials

 

 

 

1.                   Find the value of x in each of the following:

 

a)         x = log22           b)         log2x = 5           c)         -2 = log3x

 

 

 

 

2.                   Find the value of:

 

a)         log381               b)         log41                 c)         log5()

 

 

 

3.                   Simplify:

 

a)                   log105 + log1010 – log10(1/2)

b)                   log 5 + log 6 – log10 + log(1/3)

c)                   log39 – log3(1/3)

 

 

4                     Solve for x:

 

a)                   log(x + 1) + log(x – 1) = log3

b)                   log5(x + 1) + log5(x – 3) = 1

c)                   2log2x + log22 = 7

 

 

 

 

 


5.        

 

 

 

 

 

 

 

 

 

            Find the relationship between x and y.

 

 

 

 

 

 

 

 

 

 

 

6.        

 

 

 

 

 

 

 

 

 

 

 

 

 

 


            Find the relationship between x and y.

 

           

 

 

 

7.                   The population of a certain city is 80 000.  Assuming that the growth is exponential, the population P after t years is given by:

 

P = 80 000(1.2)0.1t

 

a) Find the population after 20 years

 

b) How long does it take for the population to double?