Model Answers in Ordinary National Certificate Mathematics for Engineers

D. W. Hilder, J. G. Sweetenham, C. W. Schofield, C. W. Schofield

• Publisher: Pergamon
• Year: 2014
• ISBN:
  9781483226934
• Topic: Matematica
• Subtopic: Precalcolo

Model Answers in Ordinary National Certificate Mathematics for Engineers presents a series of model answers that include all the topics covered by the many different syllabuses in Mathematics for the Ordinary National Certificate in Engineering. This book is composed 16 chapters; each chapter contains Worked Examples, Hinted Examples, and Further Examples. The opening chapters tackle the topics of logarithms, transformation and evaluation formula, progressions, binomial expansions, and algebraic equations. The succeeding chapters explore the topics of determination of laws, mensuration, equations and identities in trigonometry, solutions of triangles in trigonometry, and graphical solutions. The remaining chapters provides model answers for rates of change; maxima and minima; integration; areas, volume, centroids, and second moments of area; and Simpson's rule. This book is directed towards mathematicians, and mathematics teachers and students.

LOGARITHMS

WORKED EXAMPLES

No. 1

(a) Evaluate (i) log₄ 215, (ii) log_e 0·6.

(b) Evaluate without using tables

${\log }_{10}20+2{\log }_{10}\frac{3}{16}-\frac{1}{2}{\log }_{10}\frac{81}{64}+4{\log }_{10}2.$

(a)

(i)

$\begin{array}{ll}{\log }_{4}215\hfill & =\frac{{\log }_{10}215}{{\log }_{10}4}\hfill \\ \hfill & =\frac{2\cdot 3324}{0\cdot 6021}\hfill \\ \hfill & =\underset{¯}{\mathrm{3·87.}}\hfill \end{array}$

No.	Log
2·3324	0·3678
0·6021	$\overline{1}\cdot 7797$
3·874	0·5881

(ii)

$\begin{array}{ll}{\log }_{\text{e}}0\cdot 6\hfill & =\frac{{\log }_{10}0\cdot 6}{{\log }_{10}\text{e}}\hfill \\ \hfill & =\frac{{\log }_{10}0\cdot 6}{{\log }_{10}2\cdot 718}\hfill \\ \hfill & =\frac{\overline{1}\cdot 7782}{0\cdot 4343}=\frac{-1+0\cdot \mathrm{77...}}{}\hfill \end{array}$