HOMEWORK #15 - SOLUTIONS
Page 675
70)
2
eln 7 x = 7x 2
92)
(
)
(
)
D = 10 log 1012 I ⇒ D = 10 log 1012 ⋅ 3.2 × 10 −6 =
(
)
10 log 3.2 × 10 6 = 65.051 decibels
Page 686
6)
log (10, 000x ) = log (10, 000 ) + log x = 4 + log x
10)
⎛ x ⎞
log ⎜
= log x − log1000 = log x − 3
⎝ 1000 ⎟⎠
14)
⎛ e4 ⎞
ln ⎜ ⎟ = ln e4 − ln 8 = 4 − ln 8
⎝ 8⎠
22)
log b xy 3 = log b x + log b y 3 = log b x + 3log b y
44)
⎛ 3x + 7 ⎞
log ( 3x + 7 ) − log x = log ⎜
⎝ 7 ⎟⎠
( )
60)
1
( log 4 x − log 4 y ) + 2 log 4 ( x + 1) =
3
⎛ x⎞
⎛ x⎞
1
log 4 ⎜ ⎟ + 2 log 4 ( x + 1) = log 4 ⎜ ⎟
⎝ y⎠
⎝ y⎠
3
1
3
+ log 4 ( x + 1) =
⎡⎛ x ⎞ 1 3
⎤
2
⎢
log 4 ⎜ ⎟ ( x + 1) ⎥
⎢⎝ y ⎠
⎥
⎣
⎦
log 57.2 1.757
=
= 1.4595
log16
1.204
64)
log16 57.2 =
68)
logπ 400 =
76)
log 7 x = log 7 3 + log 7 5 ⇒ log 7 x = log 7 15 ⇒ x = 15
102) e
ln 8 x 5 −ln 2 x 2
log 400
= 5.2340
log π
=e
⎛ 8 x5 ⎞
ln ⎜ 2 ⎟
⎝ 2x ⎠
3
= eln 4 x = 4x 3
2