Practice Test #2 – NOT HOMEWORK
Name: _________________________________
Exponential and Logarithmic B
Period: ______
1. Find the multiplier in each rate of growth or decay.
a) 9.3% growth
b) .045% decay
c) 12% growth
d) 2.3% decay
2. Sketch . Describe the transformations. What is the domain and range for each?
a. y  2x 1  4
x
y
D:
R:
a. y  log 4 ( x  1)  3
x
D:
R:
y
Practice Test #2 – NOT HOMEWORK
3. Evaluate without a calculator.
a) log 2 43 x
b) 2log3 27
c) 10log5 x
d) 2log2 4 x
4. Write as a single log in simplest terms.
a) log a 2  log a 6  log a 24
b) log5 n  2log5 m  log5 p
5. Expand using the laws of logarithms.
a) log 3
1
27x 2
b) ln
3x 2
4
6. True or False? If false, give the correction.
a) log 2 3 
log 2
log 3
c) 2log a  log b  2log ab
e) log
m
 log m  (log n  log p)
np
g) log 4 16  log 4 4  2
b) ln e  1
d) log
m
 log m  log n
n
f) log10 10  log10
h) logb y  x  y  b x
Practice Test #2 – NOT HOMEWORK
7. Solve for x. Round your answers to the nearest thousandths, if necessary.
1
2
a) 4 x  48
b) log x 13 
c) log3 ( x  4)  log3  x  4   2
d) log9 ( x  7)  log9 ( x 1)  1
e) 2  3log 2
x
5
2
g) 3e x 2  1.24
i) 2 ln 3  ln
x
5
f) 2ln x  2.58
h) log5 56  x
 1 

 27 
j) 3x 2  
3x
Practice Test #2 – NOT HOMEWORK
8. Diego decided to invest his $750 tax refund rather than spending it. He found a bank that would pay
him 8.2% interest, compounded quarterly. If he deposits the entire $750 and does not deposit or
withdraw any other amount, how long will it take him to double his money in the account?
9. The number of horses in the wild in the northern section of Clark County is increasing at the rate of
0.9% per year. Your environmental studies class has counted 40 horses in the area. After how many
years will this population of 40 wolves increase to 300 horses, if this rate of increase continues?
10. The half-life of unknown element is known to be 6250 years. Doctor Frankenstein has 200 grams of
this unknown element in his experimental laboratory. If untouched, how many of the 200grams will
remain after 3000 years?