Description

                                                                MATH 30-1

                                                                ASSIGNMENT# 5

1.Convert to Exponent form

2. If, find the value of n                      

3. If  and  what is the value of                 

4.  If log3 5  =  x, express  in terms of x.

5. If logm 9 = 2 and log8n = 2, find log 2 (m n)         

6.  Find x and y if                                      

7. Determine the value of                 

8.  Write as a single logarithm    

a.

b.

c.

d.  6 + log3 (5)

e.

9. Solve. Check for restrictions if applicable

 a)     79 (3 x + 1) = 5 3x – 4

b)  142x-3 = 6 x+2

c)

d) log 49 (m +4) +  log 49 (m - 2)  =

10.  Given y = log4(x).

a. Write the equation of the transformed function after a vertical stretch by a factor of  , reflection y axis, Horizontal stretch by a factor 2 shifted right by 3 and shifted down by 2     

b. State the domain, asymptotes and intercepts                                                                          

c. Write the equation of the inverse                                                                                

11.The pH of a solution is defined as pH= -log(H+), where H+ is the hydrogen ion concentration, in moles/L. Acetic acid has a pH of 2.9. Formic acid 4 times as concentrated as acetic acid .What is the pH of a formic acid?

12.The volume, V(t) of a moth ball after t weeks of exposure to air, is given by v(t) = V0 e – 0.35 t, where V0 is the initial volume. If a moth ball with a diameter of 1.5 cm is exposed to air, what volume, to the nearest hundredth, remains after two weeks?

13.The value of a printing machine is decreasing exponentially  according to the equation

V= 75000 e – 0.14 t , where ‘t’ is the time in years                                                                 

a)      Find the value of the machine after 8 years?

b)      After how many years is the machine worth 25% of its original value?

14. The sound intensity,, in decibels is defined as, where I is the intensity of the sound, in watts/m2 and I0, the threshold of  hearing, is 10-12W/m2. In some cities, police can issue a fine to the operator of a motor cycle when the sound while idling is 20 times as intense as the sound of an automobile. If the decibel level of an automobile is 85 dB, at what decibel level can police issue a fine to a motor cycle operator?

15. Describe, in order, a series of transformations that could be applied to the graph of y = log5 x to draw the graph of each function                                                              

a.      

          b. y = - log5 (3(x-12)) + 2

c. y = log5

d. y = log 5