Name:
Logarithms #1
1) Evaluate each logarithm, if possible. If a logarithm is not defined, say so.
log 4 64
log 1 64
log 4 1
1
⎛ 1⎞
log 4
log 4 ⎜ − ⎟
4
⎝ 16 ⎠
16
log 1 4
log 4 4
log 4 4 5
log 4 4 −1
log 4 0
log 4
1
42
log 4 4 −4
log 4 (−4)
log 64
1
4
16
log 4 4 ⋅ 4
log 4 4 ⋅16
log 64 64
log 64 4
log 4
1
16
1
16
2
log 1
log 1 16
log 4 2
log 4 3 4
log b b 2
log 1
2
log b b
b
log 4 32
b3
log 1
2
e) log 5 (log 3 x) = 0 3) Simplify:
a) 10 log(7) b) log 5 25 x
f) log 6 (log 2 x) = 1
( )
4) Find the inverse of each of the following:
a) f (x) = 2 log 5 ( x − 1) log b
c) ln x = 0
d) (log x)2 =4 b5
b
2) Solve the following logarithmic equations.
a) log x = 3 b) log |x – 1| = 3
3
b) f (x) =
3
log 4
6x−3
+4
2
4
1
5
b7
Simplify:
5) 8
( )
6)
log 7 49 −3x 7) log 2 64 x −1
8) 3eln ( 20 ) 9)
log 5 (125 ) 10)
⎛ 1⎞
log 3 ⎜ ⎟
⎝ 81 ⎠
11)
log (10000 ) 12)
⎛ 1⎞
ln ⎜ ⎟ ⎝ e⎠
13)
6
14)
Find the inverse of f (x) = 3( 4 )
log 8 x 2
x−2
(
log 6 ⎡⎣ log 8 ( 2 ) ⎤⎦
)
15) a)
Graph:
f (x) = log 3 ( x + 2 ) − 3 c)
b)
f (x) = ln ( x + 2 ) + 1 f (x) = log1/2 ( x + 1) − 3