Page 135 - Mathematics_Form_Two

Logarithms

(d) log 2 8 6. Given that log2x = u and log2y = v,
write:
3
(b) log 5 (5 125 ) (a) 2 2u− 2 in terms of x
1000
(e) log 1000 (b) 2 4v+ 1 in terms of y
3
(c) log 0.0001 7. Find the value of x in each of the
3
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(f) log0.001 5 following equations:
(a) log x = log 5 2log 3+ a
a
a
3. Simplify each of the following
expressions using the laws of (b) log x = 3log 15 2log 15− a Mathematics for Secondary Schools
a
a
logarithms: (c) log x = log 4 log 5+ 3
3
3
log64
(a) (d) log x = log 2 + log5
log 4 (e) log x = log20 log200 log50− +
(b) log 28 log 7− 2
2
(f) log x = log2 log20 log5− +
(c) log 10 log 8.1+ 3
3
8. Given that log 2 = 0.30103,
(d) log 20 log50+ log 3 = 0.47712, and log 5 = 0.69897.

4
(e) log3 + log   10  81   Find the value of:
 (a) log 90
3
(f) log 4 1  6  5
log 4 (b) log    
5  5 

4. Without using a calculator, find the 9. If log y + 2log x = 3, express y in
value of 2log5 + log36 – log9. terms of x.

5. Use logarithmic laws to expand each 10. Express p in terms of q for each of
of the following expressions. the following:

⎛  x y  x y − −3 3 ⎞  u 2 v   ( x + ) y 2 2
2 2
⎟
⎟
log
(a) log ⎜ ⎜ ⎜ 25 ⎟  (b) log   zv 5   (a) log q − (c) log 4log p =   
5 
⎟
5⎜
 25 ⎠  ⎝   (b) log q + log m =  z log(m bp−  )
 x y  2 − 3  u 2 v   ( x + ) y 2 
(a) log 5   (b) log  5   (c) log 11. Solve for x given

 25    zv    z   log(x − 2) log(x− − 1) 0= .
 x y  2 − 3  u 2 v   ( x + ) y 2  12. Evaluate each of the following
(a) log 5   (b) log  5   (c) log  (a) log9(81) (c) log2(16)
 25    zv    z  
(b) log 36 (d) log8(64)
6

129
Student's Book Form Two

11/10/2024 20:13:01
MATHEMATIC F2 v5.indd 129
MATHEMATIC F2 v5.indd 129 11/10/2024 20:13:01