Download Practice 8

MAT 117
Practice 8
1) Write log 5M = x – 3 in exponential form.
2) Write 5t= V in logarithmic form.
3) Evaluate the following (Find EXACT ANSWERS, not calculator approximations.)
1
a) log 3 81
b) log 1000 c) log 4
d) log(. 001)
e) log a 3 a 7
16
5
h) log 16 128 i) log 27 3
j) log 3 9
k) log 4 (16)
f) ln e 6
g) e ln 45
4) Given f(x) = log 2 ( x 2  4 x  5) , Find the domain (interval notation)
5) Solve for x. log 4 (2x  3)  3
6) Solve for x. log x2 81  4 7) Solve for x. log 3 ( x 2  x  21)  2
Write each of the following in terms of logarithms of x, y, and z, with no product, quotient, or exponent inside
any logarithm.
 x 3 w2 
x3 x
8) log  5 
9) ln 4
3
( x  2) 5
y z 
Write the following as a single logarithm.
10) 2 log 2 3  3 log 2 y  4 log 2 x
11) 4 log( x  1)  5 log x  log( x  1)
12) Use your calculator to estimate the following to 3 decimal places.
a) log 400
b) ln 56
c) log 5 35
d) log 14 7
13) What would you type into your calculator (exactly as it would show on the screen ) to graph the function
f(x) = log 5 ( x 2  7) ?
14) Solve for x. Find the exact values.
a) e3x = 100
b) 43x = 32x+2
c) 43x – 23 = 211
d) 5x+3 = 42x + 3
15) Find the exact value of all solutions to the equation e2x – 3ex – 40 = 0.
(No decimals or calculator approximations.)
16) Find the exact values of all solutions to the following equations.
a) lnx = 4
b) log(3x – 5) + log(x +5) = 2
c) log 3 (5x  3)  log 3 ( x  3)  2
d) log 4 x  log 2 ( x  4)  2
e) log 2 3  5x  log 2 (1  x)  4
(hint for d – use the change of base formula on log4x to switch to base 2)
17) Use your graphing calculator to find all solutions to the equation x2 – 6x + 9 =
Round to 4 decimal places. (Write “No Solution” if there are no solutions)
4e– x
Solutions to Practice 8 (revision 0)
3
7
7
1
2
c) -2 d) -3 e)
f) 6
g) 45 h)
i)
j)
2
3
4
3
5
67
k) undefined 4) (,1)  (5, ) 5)
6) 5 7) -6, 5
8) 3logx + 2logw – 5logy – logz
2
9x4 
 ( x  1) 4 ( x  1) 
7
5
9) ln x  ln( x  2)
10) log 2  3 
11) log 
12a) 2.602
b) 4.025

8
12
x5
 y 


c) 2.209
d) .737
13) ln(x2 – 7) / ln(5) (or log(x2 – 7) / log(5) ) 14a) 1.535 b) 10
1) 5x – 3 = M
c) 1.312
17) -1.7153,
2) log5V = t
3a) 4 b)
 125 
ln 

3 ln 5  3 ln 4
64 
d) 
or
2 ln 4  ln 5
 16 
ln  
5
2.3966, 3.3707
15) ln8
16a) e4
b) 5
c) 6
d) 4
e) -1