Higher Engineering Mathematics, Sixth Edition
22 Higher Engineering Mathematics In Problems 12 to 18 solve the equations: log 10 x= 4 [10000] lgx= 5 [100000] log 3 x=2[9] lo ...
Logarithms 23 =6log2−7log2+5log2 by the third law of logarithms =4log2 Problem 15. Write 1 2 log16+ 1 3 log27−2log5 as the logar ...
24 Higher Engineering Mathematics 1 2 Hence, log4=logx log √ becomes 4 =logx i.e. log2=logx from which, 2 =x i.e. thesolution of ...
Logarithms 25 Rearranging gives x= log 1027 log 103 = 1. 43136 ... 0. 4771 ... = 3 which may be readily checked ( Note, ( log8 l ...
26 Higher Engineering Mathematics y 0.5 1.0 0 123 2 0.5 2 1.0 x x 3 0.48 2 0.30 1 0 0.5 2 0.30 0.2 2 0.70 0.1 y 5 log 10 x 2 1.0 ...
Chapter 4 Exponential functions 4.1 Introduction to exponential functions An exponential function is one which contains ex,e bei ...
28 Higher Engineering Mathematics Using a calculator, v=300e−^0.^1063829 ...= 300 ( 0. 89908025 ...) =269.7 volts Now try the fo ...
Exponential functions 29 whereaandkare constants. In the series of equation (1), letxbe replaced bykx. Then, aekx=a { 1 +(kx)+ ( ...
30 Higher Engineering Mathematics x − 3. 0 − 2. 5 − 2. 0 − 1. 5 − 1. 0 − 0. 5 0 ex 0.05 0.08 0.14 0.22 0.37 0.611.00 e−x 20.09 1 ...
Exponential functions 31 decay curve over the first 6seconds. From the graph, find (a) the voltage after 3.4s, and (b) the time ...
32 Higher Engineering Mathematics From the last two examples we can conclude that: logeex=x This is useful whensolving equations ...
Exponential functions 33 Taking natural logs of both sides gives: ln 7 4 =lne^3 x ln 7 4 = 3 xlne Since lne=1ln 7 4 = 3 x i.e. 0 ...
34 Higher Engineering Mathematics 5= 8 ( 1 −e −x 2 ) [1.962] ln(x+ 3 )−lnx=ln(x− 1 ) [3] ln(x− 1 )^2 −ln3=ln(x− 1 ) [4] ln(x+ ...
Exponential functions 35 Hence α= 1 θ ln R R 0 = 1 1500 ln ( 6 × 103 5 × 103 ) = 1 1500 ( 0. 1823215 ...) = 1. 215477 ···× 10 −^ ...
36 Higher Engineering Mathematics 0 2 4 6 5.71 8 0.5 0.555 i (A) 1.0 1.5 t(s) i 5 8.0 (1 2 e^2 t/CR) Figure 4.6 Problem 20. The ...
Exponential functions 37 of friction between these two surfaces is μ= 0 .26. Determine the tension on the taut side of the belt, ...
38 Higher Engineering Mathematics determine approximate values ofaandb.Also determine the value ofywhenxis 3.8 and the value ofx ...
Exponential functions 39 1000 100 Voltage, v volts 10 1 0 102030405060708090 Time, t ms A B C (36.5, 100) v 5 Ve Tt Figure 4.9 T ...
Revision Test This Revision Test covers the material contained in Chapters 1 to 4.The marks for each question are shown in brack ...
Chapter 5 Hyperbolic functions 5.1 Introduction to hyperbolic functions Functions which are associated with the geometry of the ...
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