MHF 4U
NAME:__________________________
DATE: _____________________________
REVIEW EXPONENTIAL & LOGARITHMIC FUNCTIONS
1. For each of the following functions, determine:
2 −x
i. y = (0.1) − 3
ii. y = − log 3 
1

x + 1 + 3
2

a. Equation of asymptote:
a. Equation of asymptote:
______________________
________________________
b. Range: R=
b. Domain: D=
______________________________
_______________________________
c. The function is (circle the appropriate answer):
c. The function is (circle the appropriate answer):
INCREASING
or DECREASING
INCREASING
or DECREASING
d. The y-intercept: ____________________
d. The y-intercept: ____________________
e. The x-intercept: ____________________
e. The x-intercept: ____________________
2. List, in order, the transformations that are to be applied to the base graph y = log x in order to
obtain the graph of y = log
3
0.01
.
100 x
3. Use the method discussed in class to sketch the graph of y = log 2 (− x + 4) − 2 .
4. Evaluate the following using the properties of logarithms. NO CALCULATORS.
a. 25
c.
1
log7 125
log 3 3 4
log 3 8
b. log 1
5
81
3
d.
1
1
9
log 9 18 − log 9
+ log 9
2
2
2
5. Given that log b m = 2 and log b n = 3 , evaluate the following expressions:
a.
 b 

log b 
2 
 mn 
6. Prove the following identity:
b.
(
log m 3  n
1
log  
b
)
2
1
1
−
=
log 12 2 log 4 2 log 36 2
7. How many times more intense is the sound of a subway train of 103 dB than the sound of
a conversation of 51 dB?
8. Emilio invests $1,000 at 7.5% compounded quarterly. Ho long, to the nearest month will
take for the investment to grow to $1,500?
9. Iodine-135 has a half life of 8 days. How long would it take for 28 g of iodine-135 to decay
to less than 3 g?
10.
11. Solve the following exponential and logarithmic equations. Express your answer as exact values.
a. x
1
2 − log x
2
= 100
c. log( 3x + 2) + log( x − 1) = 2
b. 2
x −1
+ 2 x −2 + 2 x −3 = 448
d. 2 log 2 x = − log 2 (6 − x 2 )