HPC Section 5.5(1)
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Transcript of HPC Section 5.5(1)
- 1. ii iii '1 'l ill Si it ill it it ill ll iii1. Use the log button on your calculator to evaluate each of the following quantities:l
- 2. ll ll '1 it It ll ll3. 12. Make a conjecture about the domain of log X. )o3. Make a conjecture about what the log X function actually does. The Pder we muse.LO to t0 get H16 number lAJe'i'i)0lLl4iL (0% Cg,
- 3. it ll '1 ii iii til itil l ll?llSi Si ll ii Jlil4. Test your conjecture with these values of X.Does your conjecture appear to be true?
- 4. iiill illit illllll ii iii ll ll ll Jlrii itUse the values in the table from part 1 to sketch the graph 0of the same set of axes. Them plot the graph
- 5. 6. Make a conjecture about the rule for f "1Incidentally,the way we should really write f(x) =logx isf(x)= log10 x. $"(x): /07. Now consider g(x) =2 .What would g1(x)be? a"(1
- 6. 9. So, ifk(x)= b"b>0,k1(x)= logbx.What are the domain andrange ofk (x) =logb x ? Domain. }5>O Range:loabgg e/ (32
7. 10. Since y =1ogb x and y =b are inverse functions of each other,the following two equations must be equivalent to one another: y= logbx and x= b". mnihm D? _This,in fact,the definition of the logarithm that you will see in your book5l"l"V 7' gr bx : > lr1lVQ)rSe:X/ /Eb} (imirbf 4 lhygre ; lD 7k' 5 6* 8. I, I Ii! II. IIII. IIl, IIl. IiII . , F-'4 -. ..< __. .< . .l U,__. ., -'r~s 7-44- MT --a -. g 'D>4- _s. ., _-_,__. ., >4-x-A,-n.>>A -. a..:4 ll .1; J;Jj J;J,, J] J,,i, , J,Jr J;J, H};J;J, I11. Use this denition to evaluate each of the following expressions: 32:2 X55a.logz 32 7- X. b.1og93 :1 :71: / /a_ 9. Two bases in particular are frequently used for logs. Common log | og10(x) is the inverse of 10*. l%, .,3C': ~l