Exponential algorithm is the power of rational number. How to simplify the operation, such as multiplication

Exponential algorithm is the power of rational number. How to simplify the operation, such as multiplication

Exponential function the general form of exponential function is y = a ^ x (a > 0 and not = 1). From the above discussion of power function, we can see that in order to make x take the whole set of real numbers as the domain of definition, we can only make the different sizes of a affect the graph of function as shown in the figure

Who knows the formula of logarithmic exponent

Basic operation:
Index: x ^ n * x ^ m = x ^ (M + n) x ^ n / x ^ m = x ^ (m-n)
Log: log (n) x + log (n) y = log (n) (XY) log (n) x-log (n) y = log (n) (x / y) log (n) x ^ y = log (n) x
There is also the formula log (x) y = log (n) y / log (n) X
Where log (n) x is the logarithm of X with n as the base
The relation between exponent and logarithm: x ^ n = y, then log (x) y = n
That's all that's commonly used

What is the formula of negative exponent?

How to calculate the time zone, that is, to give the time of one time zone and calculate the time of another time zone (to be explained in detail)

The method of calculating area time is: the area time to be calculated = known area time - (the time zone of known area time - the time zone of the area time to be calculated), (Note: the east time zone is positive, and the west time zone is negative)
Example 1: it is known that the time of Beijing (East District 8) is 12:00 on May 1. What is the district time of Tokyo (East District 9)?
Tokyo time = 12:00 - (8-9) = 13:00 (that is, Tokyo time is 13:00 on May 1)
Example 2: it is known that Beijing time is 12:00 on May 1. How about the district time of London (central time zone)?
London time = 12:00 - (8-0) = 4:00 (London time is 4:00 on May 1)
Example 3: it is known that Beijing time is 12:00 on May 1. What is the district time of New York (West District 5)?
New York time = 12:00 - [8 - (- 5)] = - 1:00 + 24:00-1 day = 23:00 (that is, New York time is 23:00 on April 30). (Note: when the calculated area time is negative, 24:00 should be added, and the date minus one day, that is, from May 1 to April 30)
Example 4: it is known that the New York time is 12:00 on May 1. What is the district time of Tokyo?
Tokyo time = 12:00 - [(- 5) - 9] = 26:00-24:00 + 1 day = 2:00, that is, Tokyo time is 2:00 on May 2. (Note: when the calculated area time is greater than or equal to 24:00, 24:00 should be subtracted, and the date plus one day, that is, from May 1 to May 2)

Time difference calculated by geographical formula

Add East and subtract West, 15 degrees an hour. Add in the east of the time zone and subtract in the West

How can geography work out time zone and time zone?

(1) for the convenience of communication, the global longitude is divided into 24 time zones. Each time zone uses the local time of its central longitude as the common area time of the whole time zone. (2) the time zone of a certain longitude is calculated: longitude / 15 = quotient If the remainder is less than 7.5, the time zone is the quotient. If the remainder is greater than 7.5, the time zone is the quotient + 1.2.zone time (1) for every zone in the time zone, the zone time difference is 1 hour, East early (more) west late (less) Note: the date of crossing the date line should be added or subtracted by one day first (2) formula calculation: time zone a - time zone B = time zone a - time zone B note: the east time zone is written as a positive number, The Western time zone is written as a negative number. The positive and negative numbers have taken into account the date difference on both sides of the solar line. 3. The local time (1) is formed according to the solar radiation, such as the meridian (located in the center of the daytime hemisphere) where the direct point of the sun is located is 12 o'clock, (2) calculation on the chart: for every 15 degree difference in longitude, the local time difference is 1 hour (or 1 degree / 4 minutes, longitude 1 minute / 4 seconds), (3) formula calculation: (a longitude - B longitude) × 1 hour / 15 degree = a local time - B local time note: the eastern longitude is written as a positive number, The west longitude is written as a negative number. The positive and negative longitudes have taken into account the date difference on both sides of the solar line. 4. The calculation method of the solar altitude angle. The difference of the solar altitude angle between the two places = the latitude difference between the two places. 5. Sunrise and sunset time (1) local time and area time calculation (2) sunrise time = (24 day length) / 2 sunrise time = 12 day length / 2 (3) sunset time = 24 sunrise time, sunset time = 12 + day length / 2 6. Midday sun height (1) midday sun height refers to the maximum sun height in a day, that is, the sun height at 12:00 local time. (2) derivation (omitted) on the figure. (3) calculation formula (compared with the direct point): 90 degrees - a place h = the absolute value of the angle difference between the direct point latitude and a place latitude skill: you can write the north latitude as a positive number, (4) calculation formula (compared with any latitude): absolute value of a H - B H = (a latitude - B latitude). Note: north latitude is written as a positive number, The geographical latitude of a day (R) is 23 ° 26 ′ n-r-june 22 * (23 ° 26 ′ 4 / 365). It shows that: (1) this formula can only roughly calculate the latitude of a day in a year; (2) if the calculation result is positive, it is the north latitude; if it is negative, it is the south latitude; (3) r is the date of a day, and r-june 22 is the number of days between that day and June 22, (23 ° 26 ′ * 4 / 365) is the latitudinal distance of the point of direct sunlight moving in one day. (assuming that it moves at a constant speed) 8. The range of polar day and polar night = 90 - the degree of the point of direct sunlight 9. The day length of a place = 24 - the day length of the same latitude but different latitude in the northern and southern hemispheres = the night length of the same latitude but different latitude in the northern and southern hemispheres 10. Night length of a place = 24 - night length of the same latitude but different latitudes of the northern and southern hemispheres = day length of the same latitude but different latitudes of the northern and southern hemispheres, that is: night length + night length of two places with the same latitude and different hemispheres = 24 hours 11. Day length, night length (1) day length = sunset time sunrise time note: it is OK to keep the same time before and after, such as local time of a place, For example, Beijing time (2) day length = (12 local time of sunrise) * 2 day length = (local time of sunset-12) * 2 note: both refer to local time of the place (3) calculation on the graph: day length = 24 hours * day arc / 360 degrees (4) day length of a place in north latitude = corresponding night length in south latitude (5) night length = 24-day length 12. The relative height formula of two points: (x-1) · h ≤ h ＜ (x + 1) · h, where h is relative height and H is contour distance, X is the number of contour lines. 13. Scale scale = distance on the map / actual distance. Note: the scale itself has no unit, but the unit of distance on the map and the actual distance should be converted and unified before calculation. The scale size is actually the degree of reduction of the actual distance, 14. Actual distance (1) actual distance = distance / scale on the map (2) on the latitude and longitude network: longitude across latitude 1 = 111 km, latitude across longitude 1 = 111 * cosa km, where a is latitude

When Jiadi (40 ° n, 30 ° E) is 6:00 on June 8, a ship is sailing on the jade Pacific Ocean, and after 10 minutes, the ship crosses the date line. At this time, the area where the ship is located may be?
A. At 15:50 on June 9, B, 15:50 on June 8, C, 16:10 on June 9,
D. June 8 16:10, e, June 7 16:10

According to CE analysis, when the time of area a (40 n, 30 E) is 6 o'clock on June 8, the time of area 12 in East China is 16 o'clock on June 8. (1) if the ship sails from west to East, that is, the ship enters area 12 in West China from East China, and the date is reduced by one day, the time of area 12 in East China may be 16:10 on June 7

Geographic time calculation
[question] at 20:10 Beijing time on April 30, 2010, what are the times in New York, Singapore, London and Brasilia?
In the answer, New York is the fifth West District, which is 4.30. Brasilia is 4.30
[question] Beijing is eight districts in the East, and five districts in the West. Isn't the time difference between the two districts 13 hours? But the time difference between the two districts is 11 hours. The same as the answer, is there something wrong with my method,

It's not from west to East, it's not 8 + 5, there's 180 ° longitude in the middle, it's 12 areas, 12-8 = 4, 12-5 = 7, so 4 + 7 = 11, so the difference is 11 hours. You should understand this time. As long as you have time to cross 180 ° longitude, you can calculate it like this, and it's easy to understand, you can understand it at a glance

How to calculate time in physical geography?
Don't master the calculation of time zone and distance?

Do less and understand more. Every 15 hours, in one time zone, one hundred and eight hours, that is, the line across the Bering Strait, one day to the East and one day to the West. On the contrary, at the meridian (0), you can ask me if you don't understand. Geography is a science in liberal arts. If you understand it, it's easy to calculate, and you don't have to memorize it

How to distinguish time zone from time zone

According to international regulations, the longitude passing through the original site of Greenwich Observatory is called 0 ° longitude, also known as prime meridian. From 0 ° longitude to East, it is called east longitude; to west, it is called west longitude. Because the earth is a sphere, there are 180 ° east longitude and 180 ° west longitude respectively. 180 ° east longitude and 180 ° west longitude are on the same longitude, that is 180 ° longitude, Each equal part is a time zone. The division of world time zone is based on the prime meridian. From 7.5 West to 7.5 east longitude (longitude interval is 15 degrees) is the zero area. From the two boundaries of zero time zone, one time zone is drawn every 15 degrees longitude, and 12 time zones are drawn from East and west respectively, The East 12 time zones coincide with the West 12 time zones, and the world is divided into 24 time zones. This is the time zone. Each time zone takes the place of the central longitude as its standard time. The standard time difference between the two adjacent time zones is one hour. Longitude zero, that is, the time of the meridian, is the world standard time. Because the meridian passes through Greenwich city near London, it is called Greenwich time, This is also British standard time, which is district time. Different time zones have different district time. Beijing longitude is 116 degrees and 21 minutes, so it is in the eighth time zone east of meridian. That is east eight time zone. 8 × 15 = 120, so the district time of East eight time zone is 120 degrees east longitude, which is Beijing time. Beijing time is the flat sun time of East 120 degrees longitude, The location of Beijing is 116 degrees 21 'east longitude, so its local sun time is about 14.5 minutes later than Beijing time. Beijing time is 8 hours earlier than world standard time