Worksheet: Logarithmic Function - Department of Mathematics

Vanier College Sec V Mathematics
Department of Mathematics 201-015-50Worksheet: Logarithmic Function
1. Find the value ofy.
(1) log
525 =y(2) log31 =y(3) log164 =y(4) log218
=y
(5) log
51 =y(6) log28 =y(7) log717
=y(8) log319
=y
(9) log
y32 = 5 (10) log9y=12
(11) log418
=y(12) log9181
=y
2. Evaluate.
(1) log
31 (2) log44 (3) log773(4)blogb3(3) log2553(4) 16log48
3. Write the following expressions in terms of logs ofx,yandz.
(1) logx2y(2) logx3y2z
(3) logpx
3py
2z
4(4) logxyz
(5) log
xyz
(6) logxy

2
(7) log(xy)13
(8) logxpz
(9) log
3px
3
pyz
(10) log4rx
3y2z
4(11) logxrpx
z
(12) logrxy
2z
8
4. Write the following equalities in exponential form.
(1) log
381 = 4 (2) log77 = 1 (3) log12
18
= 3 (4) log31 = 0
(5) log
4164
=3 (6) log6136
=2 (7) logxy=z(8) logmn=12
5. Write the following equalities in logarithmic form.
(1) 8
2= 64 (2) 103= 10000 (3) 42=116
(4) 34=181
(5)
12

5
= 32 (6)13

3
= 27 (7)x2z=y(8)px=y
6. True or False?
(1) log
xy
3
= logx3logy(2) log(ab) = logalogb(3) logxk=k
logx
(4) (loga)(logb) = log(a+b) (5)logalogb= log(ab) (6) (lna)k=k
lna
(7) log
aaa=a(8)ln1x

= lnx(9) lnpx
xk= 2k