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Logarithms (Sec. 5.3 and 5.4)
Answer True or False for 1 – 11.
_______ 1. y log 4 x is the inverse of 4
x y
_______ 2. y log 4 x is equivalent to 4
y x
_______ 3. You can take a log of a negative number.
_______ 4. The value (output) of a log can be a negative number.
_______ 5. log 0 2 1
_______ 6. log ( a y 4) log (^) a y log 4 a
_______ 7.
1/ 3 1 log log log 3 3
a a a
w w w
_______ 8.
3 log (^) a w 3log aw
_______ 9.
5 log 5 log
a
a
t
t
_______ 10. If 0 N 1 , then log N 0.
_______ 11. If log(1/ 4) x 3 , then 4
log 3 x
_______ 12. 5(7) 35
x x
_______ 13.
log log log log
a a a a
m m n n
Find a formula for
1 f ( ) x
. Also state the domain and range of f and
1 f
.
x f x 13. ( )
x f x e
- f x ( ) log 5 x 15. f x ( ) ln x
Given log 2 b w , log 3 b x , log 5 (^) b y , and log 7 (^) b z , write each of the following in
terms of w, x, y, and z.
- log 250 b 17.
log 49
b
log 7
b b
Express each of the following in terms of log a , log b , and log c. All logarithms in 19 – 21
are common logs.
5
3 2
log
c
b a
2
log 4
c b
a
log log log log 10 10 10
a b c
Write each as a single log.
22. log 4 a^ ^ log^ a^ ^ 3log^ a r log 3 a
2 3 2 log( w 1) log( w 1) log w w 1 log w 1 log w 1
24. 4log 2log log
M M (^) b bM (^) b M b b k
