Scribd
Upload
178 views2 pages

The University of Zambia: F F F F F F

This document is a tutorial sheet for a foundations mathematics and statistics course. It contains practice problems on (1) sketching graphs of functions, solving equations, and rewriting expressions between logarithmic and exponential forms. It also contains problems (2) evaluating logarithmic expressions, solving logarithmic equations, and sketching logarithmic functions on a coordinate plane. The tutorial sheet provides students with exercises to reinforce their skills in topics including functions, equations, logarithms, and their graphical representations.

Uploaded by

Hendrix Nail
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
178 views2 pages

The University of Zambia: F F F F F F

This document is a tutorial sheet for a foundations mathematics and statistics course. It contains practice problems on (1) sketching graphs of functions, solving equations, and rewriting expressions between logarithmic and exponential forms. It also contains problems (2) evaluating logarithmic expressions, solving logarithmic equations, and sketching logarithmic functions on a coordinate plane. The tutorial sheet provides students with exercises to reinforce their skills in topics including functions, equations, logarithms, and their graphical representations.

Uploaded by

Hendrix Nail
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

THE UNIVERSITY OF ZAMBIA

Department of Mathematics and Statistics


MAT1110: Foundation Mathematics and Statistics for Social Sciences
Tutorial Sheet 7 (2020/2021)
1. Sketch the graph of each of the following:

(a) i. vi.  x
f(x) = 3x f(x) =
1
ii. 4
f(x) = −3x vii.  x
f(x) = −
iii. 1
f(x) = 4−x 4
iv. viii.
f(x) = 3x + 2 f(x) = 2x−1
v. ix.
f(x) = 3x − 2 f(x) = 2x+1

(b) Solve each of the following equations:

i. iv.
3x = 81 2x = 0.125
ii. v.
x = 125
3 274x = 9x+1
iii.  x vi.  −2t
= 2t+3
1 1 1
=
2 16 8

(c) Solve each of the following equations:

i. iii.
x
2 2x
+ 3(2 ) − 4 = 0 4x − 6(2x ) − 16 = 0
ii. iv.
4x − 2x+1 = 48 22x+1 − 2x+1 + 1 = 2x

2. (a) Write each of the following in logarithm form:

i. iii.
x+2
y=5 y = ex
ii.  −2
3 16 iv.
8−1 = 0.125
=
4 9

(b) Write each of the following in exponential form:

i. iii.
log2 32 = 5 1
log27 3 =
ii. 3
 
= −4
1
log2
16
(c) Evaluate each of the following:

i. ii. iii.  
1
log6
log3 9 log5 125 36

3. (a) Solve each of the following equations:

i. iii. v.
log3 x = 4 loga 2 =
1 ln x = −2
2
ii.
iv.
log4 x =
3
2 log2 (3x + 4) = 4

(b) Solve each of the following equations:

i. iv.
log3 y = 2 log3 7 log3 (x 2 + 2) = 1 + log3 (x + 2)
ii.
log5 x − log5 4 = 2 v.
iii.
logx 8 + logx 4 = 5 log4 (x 2 + 8x − 1) = 2 + log4 (x − 1)

(c) Sketch each of the following in the indicated interval:

i. iii.
f(x) = log7 x f(x) = − log3 x
ii. iv.
f(x) = log 71 x f(x) = log 31 x

(d) Sketch the graph of f and g on the same coordinate plane.


i.
f(x) = 3x , g(x) = log3 x
ii.  x
f(x) = , g(x) = log 21 x
1
2
iii.
f(x) = ex , g(x) = ln x

You might also like