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Logarithmic growth

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phase, the number of new cells appearing is proportional to the population. This terminological confusion between logarithmic growth and exponential growth may be explained by the fact that exponential growth curves may be straightened by plotting them using a
166: 93: 51:). Any logarithm base can be used, since one can be converted to another by multiplying by a fixed constant. Logarithmic growth is the inverse of 194:
roulette system, where the potential winnings before bankruptcy grow as the logarithm of the gambler's bankroll. It also plays a role in the
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is the base of the number system used, e.g. 10 for decimal arithmetic. In more advanced mathematics, the
195: 332: 251: 416: 386: 359: 305: 278: 8: 451: 63: 227: 52: 426: 392: 365: 338: 311: 284: 257: 215: 161:{\displaystyle 1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+\cdots } 210: 180: 412: 445: 184: 230: β€“ Inverse function to a tower of powers (an even slower growth model) 206: 202: 176: 81: 28: 179:, growth are very desirable indications of efficiency, and occur in the 172: 36: 175:, logarithmic growth, and related variants, such as log-linear, or 35:
describes a phenomenon whose size or cost can be described as a
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Logarithmic growth can lead to apparent paradoxes, as in the
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Mathematical Mysteries: The Beauty and Magic of Numbers
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A familiar example of logarithmic growth is a number,
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is sometimes called logarithmic growth. During this
205:, the rapidly growing exponential growth phase of a 303: 160: 443: 171:grow logarithmically. In the design of computer 16:Growth at a rate that is a logarithmic function 384: 304:Salomon, David; Motta, G.; Bryant, D. (2007), 253:Programming With C++ And Data Structures, 1E 364:, Cambridge University Press, p. 94, 307:Data Compression: The Complete Reference 245: 243: 18: 411: 330: 276: 444: 385:Friedman, Craig; Sandow, Sven (2010), 249: 357: 240: 418:More Fallacies, Flaws & Flimflam 423:Mathematical Association of America 13: 14: 463: 388:Utility-Based Learning from Data 283:, Career Press, pp. 57–58, 183:analysis of algorithms such as 405: 378: 351: 337:, Da Capo Press, p. 112, 324: 297: 270: 1: 234: 39:function of some input. e.g. 23:A graph of logarithmic growth 7: 331:Clawson, Calvin C. (1999), 221: 10: 468: 391:, CRC Press, p. 97, 361:Understanding Probability 310:, Springer, p. 49, 277:Szecsei, Denise (2006), 196:St. Petersburg paradox 162: 24: 218:for the growth axis. 163: 22: 358:Tijms, Henk (2012), 94: 66:, which grows as log 250:Litvin, G. (2009), 64:positional notation 413:Barbeau, Edward J. 228:Iterated logarithm 158: 55:and is very slow. 53:exponential growth 33:logarithmic growth 25: 216:logarithmic scale 150: 137: 124: 111: 459: 437: 435: 409: 403: 401: 382: 376: 374: 355: 349: 347: 328: 322: 320: 301: 295: 293: 274: 268: 266: 247: 211:bacterial growth 167: 165: 164: 159: 151: 143: 138: 130: 125: 117: 112: 104: 467: 466: 462: 461: 460: 458: 457: 456: 442: 441: 440: 433: 410: 406: 399: 383: 379: 372: 356: 352: 345: 329: 325: 318: 302: 298: 291: 275: 271: 264: 248: 241: 237: 224: 181:time complexity 142: 129: 116: 103: 95: 92: 91: 86:harmonic series 71: 17: 12: 11: 5: 465: 455: 454: 439: 438: 431: 425:, p. 52, 404: 397: 377: 370: 350: 343: 323: 316: 296: 289: 269: 262: 238: 236: 233: 232: 231: 223: 220: 169: 168: 157: 154: 149: 146: 141: 136: 133: 128: 123: 120: 115: 110: 107: 102: 99: 67: 15: 9: 6: 4: 3: 2: 464: 453: 450: 449: 447: 434: 432:9780883855805 428: 424: 420: 419: 414: 408: 400: 398:9781420011289 394: 390: 389: 381: 373: 371:9781107658561 367: 363: 362: 354: 346: 344:9780738202594 340: 336: 335: 327: 319: 317:9781846286032 313: 309: 308: 300: 292: 290:9781564149145 286: 282: 281: 273: 265: 263:9788125915454 259: 255: 254: 246: 244: 239: 229: 226: 225: 219: 217: 212: 208: 204: 199: 197: 193: 188: 186: 185:binary search 182: 178: 174: 155: 152: 147: 144: 139: 134: 131: 126: 121: 118: 113: 108: 105: 100: 97: 90: 89: 88: 87: 83: 79: 75: 70: 65: 61: 56: 54: 50: 46: 43: =  42: 38: 34: 30: 21: 417: 407: 387: 380: 360: 353: 333: 326: 306: 299: 279: 272: 252: 207:cell culture 203:microbiology 200: 189: 177:linearithmic 170: 82:partial sums 77: 73: 68: 59: 57: 48: 44: 40: 32: 26: 47: log ( 29:mathematics 452:Logarithms 235:References 192:martingale 173:algorithms 156:⋯ 76:), where 37:logarithm 446:Category 415:(2013), 280:Calculus 222:See also 84:of the 72: ( 429:  395:  368:  341:  314:  287:  260:  62:, in 427:ISBN 393:ISBN 366:ISBN 339:ISBN 312:ISBN 285:ISBN 258:ISBN 201:In 27:In 448:: 421:, 242:^ 198:. 187:. 31:, 436:. 402:. 375:. 348:. 321:. 294:. 267:. 153:+ 148:5 145:1 140:+ 135:4 132:1 127:+ 122:3 119:1 114:+ 109:2 106:1 101:+ 98:1 78:b 74:N 69:b 60:N 49:x 45:C 41:y

Index


mathematics
logarithm
exponential growth
positional notation
partial sums
harmonic series
algorithms
linearithmic
time complexity
binary search
martingale
St. Petersburg paradox
microbiology
cell culture
bacterial growth
logarithmic scale
Iterated logarithm


Programming With C++ And Data Structures, 1E
ISBN
9788125915454
Calculus
ISBN
9781564149145
Data Compression: The Complete Reference
ISBN
9781846286032
Mathematical Mysteries: The Beauty and Magic of Numbers

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