2222:
2298:
75:
31:
2254:
2265:
Notice that while the horizontal (time) axis is linear, with the dates evenly spaced, the vertical (cases) axis is logarithmic, with the evenly spaced divisions being labelled with successive powers of two. The semi-log plot makes it easier to see when the infection has stopped spreading at its
1574:
2187:
1167:
1737:
892:
2266:
maximum rate, i.e. the straight line on this exponential plot, and starts to curve to indicate a slower rate. This might indicate that some form of mitigation action is working, e.g. social distancing.
1939:
402:
1302:
1256:
260:
1839:
988:
724:
2024:
554:
193:
631:
2378:
316:
2042:
283:
999:
2353:
2290:
and nutrient exhaustion is commonly illustrated by a semi-log plot. Time is usually the independent axis, with the logarithm of the number or mass of
2416:
1268:
times the slope of the straight line of its lin–log graph, plus a constant. Specifically, a straight line on a lin–log plot containing points (
1175:
2258:
2370:
1644:
799:
1569:{\displaystyle F(x)=(F_{1}-F_{0}){\left}+F_{0}=(F_{1}-F_{0})\log _{\frac {x_{1}}{x_{0}}}{\left({\frac {x}{x_{0}}}\right)}+F_{0}}
2421:
1861:
324:
201:
1748:
903:
2345:
637:
2411:
1950:
458:-axis) is proportional to the logarithm of the number, not the number itself. It is equivalent to converting the
492:
159:
2279:
573:
150:
2294:
or other microbe as the dependent variable. This forms a plot with four distinct phases, as shown below.
2247:
288:
2317:
2287:
2253:
318:
vertical intercept. The logarithmic scale is usually labeled in base 10; occasionally in base 2:
2182:{\displaystyle F(x)={F_{0}}n^{\left({\frac {x-x_{0}}{x_{1}-x_{0}}}\right)\log _{n}(F_{1}/F_{0})}}
146:
138:
79:
35:
2323:
1162:{\displaystyle F_{1}=m\log _{n}(x_{1}/x_{0})+F_{0}=m\log _{n}(x_{1})-m\log _{n}(x_{0})+F_{0}}
467:
268:
195:
form straight lines when plotted semi-logarithmically, since taking logs of both sides gives
2210:, a plot of logarithm of pressure against temperature can be used to illustrate the various
2406:
2320:, for converting a nonlinear form to a semi-log form amenable to non-iterative calculation
2221:
2211:
2400:
2230:
2226:
2297:
142:
115:
2250:, there are times when other bases are more appropriate, as in this example:
1620:), somewhere on the straight line in the above graph, and further some other
775:), somewhere on the straight line in the above graph, and further some other
2311:
2207:
470:
uses the logarithmic scale for both axes, and hence is not a semi-log plot.
2291:
2283:
560:
479:
74:
30:
17:
2275:
2203:
111:
416:
83:
43:
2296:
2252:
2220:
2215:
1584:
On a log–linear plot (logarithmic scale on the y-axis), pick some
73:
29:
466:
values) to their log, and plotting the data on linear scales. A
1732:{\displaystyle m={\frac {\log _{n}(F_{1}/F_{0})}{x_{1}-x_{0}}}}
887:{\displaystyle m={\frac {F_{1}-F_{0}}{\log _{n}(x_{1}/x_{0})}}}
2234:
2371:"Interesting semi-logarithmic graph – YouTube Traffic Rank"
482:
axis is scaled logarithmically (with a logarithmic base of
411:(sometimes log–lin) plot has the logarithmic scale on the
1934:{\displaystyle {\frac {F_{1}}{F_{0}}}=n^{m(x_{1}-x_{0})}}
397:{\displaystyle \log(y)=(\gamma \log(a))x+\log(\lambda ).}
563:
axis logarithmically scaled (with a logarithmic base of
2029:
This can be generalized for any point, instead of just
1638:) on the same graph. The slope formula of the plot is:
793:) on the same graph. The slope formula of the plot is:
478:
The equation of a line on a linear–log plot, where the
1251:{\displaystyle F(x)=m\log _{n}(x)+\mathrm {constant} }
559:
The equation for a line on a log–linear plot, with an
255:{\displaystyle \log _{a}y=\gamma x+\log _{a}\lambda .}
78:
The linear–log type of a semi-log graph, defined by a
34:
The log–linear type of a semi-log graph, defined by a
2045:
1953:
1864:
1834:{\displaystyle \log _{n}(F_{1}/F_{0})=m(x_{1}-x_{0})}
1751:
1647:
1305:
1178:
1002:
906:
802:
640:
576:
495:
327:
291:
271:
204:
162:
2257:A semi-logarithmic plot of cases and deaths in the
983:{\displaystyle F_{1}-F_{0}=m\log _{n}(x_{1}/x_{0})}
450:On a semi-log plot the spacing of the scale on the
427:(sometimes lin–log) is the opposite. The naming is
2346:"Graphs on Logarithmic and Semi-Logarithmic Paper"
2181:
2018:
1933:
1833:
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1568:
1250:
1161:
982:
886:
718:
625:
548:
396:
310:
277:
254:
187:
1855:. Therefore, the logs can be inverted to find:
719:{\displaystyle F(x)=n^{mx+b}=(n^{mx})(n^{b}).}
2019:{\displaystyle F_{1}=F_{0}n^{m(x_{1}-x_{0})}}
8:
730:Finding the function from the semi–log plot
2168:
2159:
2153:
2137:
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2107:
2095:
2082:
2077:
2066:
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2005:
1992:
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1822:
1809:
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1054:
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1023:
1007:
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971:
962:
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905:
872:
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841:
829:
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809:
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685:
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581:
575:
545:
518:
494:
326:
296:
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270:
237:
209:
203:
176:
161:
2214:of a substance, as in the following for
86:scale on the y axis. Plotted lines are:
2335:
549:{\displaystyle F(x)=m\log _{n}(x)+b.\,}
50:-axis (horizontal). Plotted lines are:
2381:from the original on February 26, 2021
188:{\displaystyle y=\lambda a^{\gamma x}}
7:
1264:is proportional to the logarithm of
626:{\displaystyle \log _{n}(F(x))=mx+b}
2369:Bourne, Murray (January 25, 2007).
2356:from the original on August 6, 2021
2318:Nonlinear regression#Transformation
2259:2009 outbreak of influenza A (H1N1)
1244:
1241:
1238:
1235:
1232:
1229:
1226:
1223:
25:
311:{\displaystyle \log _{a}\lambda }
2225:log–linear pressure–temperature
739:On a linear–log plot, pick some
153:covers a large range of values.
2417:Statistical charts and diagrams
2375:SquareCirclez: The IntMath blog
2174:
2146:
2055:
2049:
2011:
1985:
1926:
1900:
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1802:
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1491:
1465:
1438:
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1315:
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1032:
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697:
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527:
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499:
388:
382:
367:
364:
358:
346:
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334:
1:
2246:While ten is the most common
145:. It is useful for data with
2242:2009 "swine flu" progression
439:), the opposite order from (
90: = 10 (red),
54: = 10 (red),
2282:, the change in numbers of
2438:
1296:) will have the function:
265:This is a line with slope
156:All equations of the form
2314:, more complicated graphs
149:relationships, where one
42:-axis (vertical), and a
2350:Interactive Mathematics
278:{\displaystyle \gamma }
2422:Non-Newtonian calculus
2302:
2301:Bacterial growth curve
2280:biological engineering
2262:
2238:
2198:Phase diagram of water
2183:
2020:
1935:
1835:
1733:
1570:
1252:
1163:
984:
888:
720:
627:
550:
398:
312:
279:
256:
189:
107:
71:
2300:
2256:
2224:
2184:
2021:
1936:
1836:
1734:
1571:
1253:
1164:
985:
889:
721:
628:
551:
399:
313:
280:
257:
190:
82:on the x axis, and a
77:
33:
2288:asexual reproduction
2043:
1951:
1862:
1749:
1645:
1303:
1176:
1000:
904:
800:
638:
574:
493:
325:
289:
269:
202:
160:
2377:. www.intmath.com.
2352:. www.intmath.com.
2193:Real-world examples
2303:
2263:
2239:
2179:
2016:
1931:
1831:
1729:
1566:
1248:
1159:
980:
884:
716:
623:
546:
394:
308:
275:
252:
185:
137:has one axis on a
108:
72:
2412:Technical drawing
2233:indicate various
2127:
1887:
1727:
1609:is shorthand for
1546:
1520:
1442:
1172:which means that
882:
764:is shorthand for
141:, the other on a
139:logarithmic scale
102: = log(
80:logarithmic scale
66: = log(
36:logarithmic scale
16:(Redirected from
2429:
2391:
2390:
2388:
2386:
2365:
2363:
2361:
2340:
2270:Microbial growth
2188:
2186:
2185:
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2177:
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2158:
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2100:
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2083:
2072:
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1963:
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1260:In other words,
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128:semi-logarithmic
21:
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2200:
2195:
2164:
2149:
2133:
2116:
2103:
2102:
2091:
2084:
2078:
2073:
2062:
2041:
2040:
2034:
2001:
1988:
1977:
1967:
1954:
1949:
1948:
1916:
1903:
1892:
1877:
1867:
1860:
1859:
1854:
1818:
1805:
1783:
1768:
1752:
1747:
1746:
1742:which leads to
1716:
1703:
1702:
1688:
1673:
1657:
1656:
1643:
1642:
1637:
1630:
1622:arbitrary point
1619:
1608:
1601:
1594:
1582:
1580:log–linear plot
1556:
1536:
1527:
1510:
1500:
1494:
1481:
1468:
1452:
1428:
1413:
1397:
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1324:
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1066:
1050:
1035:
1019:
1003:
998:
997:
967:
952:
936:
920:
907:
902:
901:
897:which leads to
868:
853:
837:
836:
825:
812:
811:
798:
797:
792:
785:
777:arbitrary point
774:
763:
756:
749:
737:
735:Linear–log plot
732:
700:
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577:
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62: (green),
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11:
5:
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2315:
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2268:
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2240:
2231:Roman numerals
2229:of water. The
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106:) (blue).
70:) (blue).
26:
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2228:
2227:phase diagram
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27:Type of graph
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2383:. Retrieved
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2358:. Retrieved
2349:
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2324:Log–log plot
2273:
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429:output–input
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2385:October 26,
2360:October 26,
2344:Bourne, M.
1586:fixed point
741:fixed point
462:values (or
147:exponential
116:engineering
2401:Categories
2330:References
2235:ice phases
454:-axis (or
425:linear–log
409:log–linear
2312:Nomograph
2208:chemistry
2144:
2114:−
2089:−
1999:−
1914:−
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474:Equations
423:-axis; a
386:λ
380:
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350:γ
332:
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273:γ
247:λ
244:
225:γ
216:
178:γ
170:λ
98:(green),
2379:Archived
2354:Archived
2306:See also
2292:bacteria
2284:microbes
561:ordinate
480:abscissa
151:variable
18:Semi-log
2286:due to
2276:biology
2204:physics
1289:,
1282:) and (
1275:,
112:science
38:on the
2407:Charts
2212:phases
417:linear
84:linear
44:linear
2216:water
135:graph
124:graph
2387:2021
2367:(2)
2362:2021
2342:(1)
2278:and
2248:base
2206:and
285:and
131:plot
118:, a
114:and
2274:In
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2135:log
1944:or
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