1 / 23

EXPONENTS AND LOGARITHMS

EXPONENTS AND LOGARITHMS. e. e is a mathematical constant ≈ 2.71828… Commonly used as a base in exponential and logarithmic functions: exponential function – e x natural logrithm – log e x or lnx follows all the rules for exponents and logs. EXPONENTS.

garin
Download Presentation

EXPONENTS AND LOGARITHMS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. EXPONENTS AND LOGARITHMS

  2. e e is a mathematical constant ≈ 2.71828… Commonly used as a base in exponential and logarithmic functions: exponential function – ex natural logrithm – logex or lnx follows all the rules for exponents and logs

  3. EXPONENTS an where a is the base and x is the exponent an = a · a · a · … · a e3 = e * e * e a1 = a e1 = e a0 = 1 e0 = 1 a-n = e-2 =

  4. EXPONENTS Using your calculator: 10x: base 10 ex: base e yx: base y Try: e2 = e1.5 =

  5. LAWS OF EXPONENTS The following laws of exponents work for ANY exponential function with the same base

  6. LAWS OF EXPONENTS aman = am+n e3e4 = e3+4 = e7 exe4 = ex+4 a2e4 = a2e4 Try: e7e11 eyex

  7. LAWS OF EXPONENTS (am)n = amn (e4)2 = e4*2 = e8 (e3)3 = e3*3 = e9 (108)5 = 108*5 = 1040 Try: (e2)2 (104)2

  8. LAWS OF EXPONENTS (ab)n = anbn (2e)3 = 23e3 = 8e3 (ae)2 = a2e2 Try: (ex)5 2(3e)3 (7a)2

  9. LAWS OF EXPONENTS Try:

  10. LAWS OF EXPONENTS Try:

  11. LAWS OF EXPONENTS Try these:

  12. LOGARITHMS The logarithm function is the inverse of the exponential function. Or, to say it differently, the logarithm is another way to write an exponent. Y = logbx if and only if by = x So, the logarithm of a given number (x) is the number (y) the base (b) must be raised by to produce that given number (x)

  13. LOGARITHMS Logarithms are undefined for negative numbers Recall, y= logbx if and only if by = x blogbx = x eloge2 = eln2 = 2 (definition ) logaa= 1 logee = lne = 1 (lne = 1 iff e1 = e) loga1 = 0 loge1 = ln1 = 0 (ln1 = 0 iff e0 = 1)

  14. LOGARITHM Using your calculator: LOG: this is log10 aka the common log LN: this is loge aka the natural log x < 1, lnx < 0; x > 1, lnx > 0 Try: ln 0 = ln 0.000001 = ln 1 = ln 10 =

  15. LAWS OF LOGARITHMS logb(xz) = logbx + logbz ln(1*2) = ln1 + ln2 = 0 + ln2 = ln2 ln(3*2) = ln3 + ln2 ln(3*3) = ln3 + ln3 = 2(ln3) Try: ln(3*5) = ln(2x) =

  16. LAWS OF LOGARITHM logb= logbx– logbz loge = ln2 – ln3 loge = ln3 – ln5 Try: ln = ln =

  17. LAWS OF LOGARITHMS logb(xr) = rlogbxfor every real number r loge(23) = 3ln2 loge(32) = 2ln3 Try: loge42 = logex3 = ln3x =

  18. ln and e Recall, ln is the inverse of e Try: x = 2 x = 0.009

  19. EXAMPLES OF LOGARITHMS Try: w/o calculator lne5 rewrite in condensed form: 2lnx + lny +ln8 3ln5 – ln19 expand: ln10x3

  20. RADICALS is called a radical a is the radicand n is the index of the radical is the radical sign by convention and is called square root

  21. LAWS OF RADICALS Laws of radicals follow the laws of exponents: Try:

  22. SCIENTIFIC NOTATION Numbers written in the form a x 10b when b is positive – move decimal point b places for the right when b is negative – move decimal point b places to the left Reverse the procedure for number written in decimal form Follows the laws of exponents

  23. EXAMPLES OF SCIENTIFIC NOTATION 1,003,953.79 1.00395379 x 106 -29,000.00 -2.9 x 104 0.0000897 8.97 x 10-5

More Related