In Exercises 1-40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln [ x 3 x 2 + 1 ( x + 1 ) 4 ]
In Exercises 1-40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln [ x 3 x 2 + 1 ( x + 1 ) 4 ]
Solution Summary: The author explains that the expanded form of the expression is 3mathrmlnx+12
In Exercises 1-40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
1) Express these large and small numbers from the Read and Study section in scientific
notation:
(a) 239,000 miles
(b) 3,800,000,000,000 sheets of paper
(c) 0.0000000000000000000000167 grams
2) Find all values for the variable x that make these equations true.
(a) 5x = 1
(b) 3x = 1/1
9
(c) 4* = 11/
4
(e) 4* = 64
(g) 10x = 1,000,000
(d) 3x=-3
(f) 2x =
=
8
(h) 10x = 0.001
(b)
4) Find an equation to fit each of the following graphs:
(a)
20
20
18
16
14
12
10
8
6
4
2
24
22
20
18
16
14
12
10
8
16
A
2
-3 -2
-1-0
2
3
4.
-1
0
1
2
3.
-2
-2
3) Which of the following are equivalent to 3? (There may be more than one that is
equivalent!)
-1
(a) (9)¯¹
3.
(b) (-3)-1
(c) (-3)
-1
(d) -(¯3)
(e) 11
3-1
(f) 3-4
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