Интегрална дефиниция на логаритмична функция - MathHelpPlanet
Знаем, че при 0" png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAQCAMAAABncAyDAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADbQS4qAAAAAEHRSTlMAMRDQiiHowAFBoWFRoLFx3e b7ogAAAMZJREFUKM+ 1UksSwyAIVUHAX+T+p602mTYkdqZd1AUL5fk+4NzfjiQvv/QXwkz++/6kyblOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSDCDqDtDhO3ASgOypGJbMyVh4A3A8bB pQq1URM1exAEcTUHaF4 R5ZzFQXDE+FuDIfET4AiqZFe+PykiQHYIbb8rAgTsAM3lvTjvc5DCVeORANFjSxbhfOqn6ux5wPICRojOf2fJ81Uscj+bmEUc5q4jKCXucmPQAaYQaRCPmIUQAAAABJRU 5ErkJggg==" /> равенство
Това ни позволява да дадем нова дефиниция на логаритмичната функция, която не се основава на концепцията за експоненциална функция. А именно, приемаме по дефиниция, че при 0" png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAQCAMAAABncAyDAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADbQS4qAAAAAEHRSTlMAMRDQiiHowAFBoWFRoLFx3eb7 ogAAAMZJ REFUKM+1UksSwyAIVUHAX+T+p602mTYkdqZd1AUL5fk+4NzfjiQvv/QXwkz++/6kyblOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSDCDqDtDhO3ASgOypGJbMyVh4A3A8bBpQq 1URM1exAEc /&g t;
Въз основа на това определение извеждаме свойствата на логаритмичната функция.
а) Логаритмичната функция е дефинирана за всички положителни стойности на . Действително, функцията е непрекъсната при 0"png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAQCAMAAABncAyDAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADbQS4qAAAAAEHRSTlMAMRDQiiHowAFBoWFRoLFx3eb7ogAAAMZJREFUKM+1UksS wyAIV UHAX+T+p602mTYkdqZd1AUL5fk+4NzfjiQvv/QXwkz++/6kyblOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSDCDqDtDhO3ASgOypGJbMyVh4A3A8bBpQq1URM1exAEcTUHaF4R 5ZzFQXDE +FuDIfET4AiqZFe+PykiQHYIbb8rAgTsAM3lvTjvc5DCVeORANFjSxbhfOqn6ux5wPICRojOf2fJ81Uscj+bmEUc5q4jKCXucmPQAaYQaRCPmIUQAAAABJRU5ErkJggg==" /> интеграл съществува за всички 0" png; base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAQCAMAAABncAyDAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADbQS4qAAAAAEHRSTlMAMRDQiiHowAFBoWFRoLFx3eb7ogAAAMZJREFUKM +1 UksSwyAIVUHAX+T+p602mTYkdqZd1AUL5fk+4NzfjiQvv/QXwkz++/6kyblOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSDCDqDtDhO3ASgOypGJbMyVh4A3A8bBpQq1URM1exAEcTUHa F 4R5ZzFQXDE+FuDIfET4AiqZFe+PykiQHYIbb8rAgTsAM3lvTjvc5DCVeORANFjSxbhfOqn6ux5wPICRojOf2fJ81Uscj+bmEUc5q4jKCXucmPQAaYQaRCPmIUQAAAABJRU5ErkJggg==" /> .
б) Логаритмичната функция е диференцируема и нейната производна във всяка точка 0" LFx3eb7ogAAAMZJREFUKM+1UksSwyAIVUHAX+T+p602mTYkdqZd1AUL5fk+4NzfjiQvv/QXwkz++/6kyblOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSD CDqDtDhO3ASgOypGJbMyVh4A3A8bB pQq1URM1exAEcTUHaF4R5ZzFQXDE+FuDIfET4AiqZFe+PykiQHYIbb8rAgTsAM3lvTjvc5DCVeORANFjSxbhfOqn6ux5wPICRojOf2fJ81Uscj+bmEUc 5q4jKCXucmPQAaYQaRCPmIUQAAAABJRU5E rkJggg==" /> е равно на
Действително, функцията е непрекъсната при 0"png;base64,iVBORw0KGgoAAAANSUhEUgAAACwAAAAQBAMAAACfEoDkAAAAMFBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAALTPQ5AAAEHRSTlMA/gFBIaWBaRFRwJEx0cHgwiZ3qgAAAL5JREFUGNNjYCAWcN i AqQo04fqtT4AkpySqKKcMQ74CAwO3CIgzrQEmzLeAwbGAgUH3A4jDftsBKtwYwKAYwOCWeK0AxFN+ChU3TGBQfMTgnFh8gAEibgAXFmJg2AgzlTnKCERNBAsz3VWAWcYSZwBXzSENdxpL 7AS o8CckZ7NADHEEumQB0NnsBRArV0Gs1F/AcLCAgVWgC2wn81KoA9lFGBIbGJhF14A5V2HeYdhfLQMke8DsaXBRBp7KBgYA/b0ohK58g2cAAAAASUVORK5CYII=" /> ограничение, което имаме:
Тъй като всяка диференцируема функция е непрекъсната, логаритмичната функция е непрекъсната при 0" png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAQCAMAAABncAyDAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADbQS4qAAAAAEHRSTlMAMRDQiiHowAFBoWFR o LFx3eb7ogAAAMZJREFUKM+1UksSwyAIVUHAX+T+p602mTYkdqZd1AUL5fk+4NzfjiQvv/QXwkz++/6kyblOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSDCDqDtDhO3ASgOypGJbMyVh4A3 A8b BpQq1URM1exAEcTUHaF4R5ZzFQXDE+FuDIfET4AiqZFe+PykiQHYIbb8rAgTsAM3lvTjvc5DCVeORANFjSxbhfOqn6ux5wPICRojOf2fJ81Uscj+bmEUc5q4jKCXucmPQAaYQaRCPmIUQA AAABJRU5 ErkJggg==" />.
в) Логаритмичната функция стриктно нараства при 0" png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAQCAMAAABncAyDAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADbQS4qAAAAEHRSTlMAMRDQiiHowAFBoWFRoLFx3 eb7ogAAAMZ JREFUKM+1UksSwyAIVUHAX+T+p602mTYkdqZd1AUL5fk+4NzfjiQvv/QXwkz++/6kyblOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSDCDqDtDhO3ASgOypGJbMyVh4A3A8bB pQq1URM1exAE cTUHaF4R5ZzFQXDE+FuDIfET4AiqZFe+PykiQHYIbb8rAgTsAM3lvTjvc5DCVeORANFjSxbhfOqn6ux5wPICRojOf2fJ81Uscj+bmEUc5q4jKCXucmPQAaYQaRCPmIUQAAAABJRU 5ErkJggg==" /& gt;. Наистина, ако 0png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAQCAMAAABncAyDAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADbQS4qaAAAAEHRSTlMAMRDQiiHowAFBoWFRoLFx3eb7ogAAAM ZJREFUKM+1UksS wyAIVUHAX+T+p602mTYkdqZd1AUL5fk+4NzfjiQvv/QXwkz++/6kyblOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSDCDqDtDhO3ASgOypGJbMyVh4A3A8bBpQq1URM 1exAEcTUHaF4R5Z zFQXDE+FuDIfET4AiqZFe+PykiQHYIbb8rAgTsAM3lvTjvc5DCVeORANFjSxbhfOqn6ux5wPICRojOf2fJ81Uscj+bmEUc5q4jKCXucmPQAaYQaRCPmIUQAAAABJRU5ErkJggg ==" />, до 0" png;base64,iVBORw0KGgoAAAANSUhEUgAAADcAAAAqBAMAAADlvd4wAAAALVBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACttl6nAAAADnRSTlMAAcR+npNbQuchQRIxsc77gUkAAAEESURB VD jLY2AgBJgP4JYz7SvAKcdoFleAx1g7GkkuGAA7yZUs03PGGbiMxsbGCRii4gvh8hhybK0RuD0/I4GtE1WEJxLO9GNgfIqmvsgTxmoSYNQQQJOtVyeIMD4SYNRDl2SYApHlAUluwHDJlDaQL N cjBgY9YNCkhoIBXNlkNSTJFBcwgEtuBklyY7WTYaoaSIwRm2sZpqiBQ4sR6M8n6HIlUK8wrFvA9QpNbpE7jCXWbIEWGTyeiKialoknAQgKMFAIuDcwTsApd7c1SRWXJMuBdYp9uCRLGdZl K+NJ txMEcWdtDdx+4gEG8S5cknFpjxnMcElemtQsdgGX5Nk7Z3E4FgBqgD9BMpumtQAAAABJRU5ErkJggg==" style="vertical-align: middle;" />, т. е. Добре дошли в заснежената зона. Следвателно, функцията строго възстановява.
г) Малък и малко по-малък от 0" png;base64,iVBORw0KGgoAAAANSUhEUg AAAEQAAAAQBAMAAABdIsRgAAAALVBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD3RSTlMAwAH/RIFqIaExENCxkemAe0WOAAABE0lEQV Qoz2NgIAxqZBXwyHJ5AollD/EpybuxE0g K4lHCYskQtwCbEtcFMBbPBobiBCxKmNgkCqBMZQEG5QMMTIIKiZKOoiCNa0XZZMEyKjA1zgcYlB8BlTD4GCZNvgB0/UltUT8HiBpBCO0cwKBsBLKI xYKB8QEDA4cD46PmCRDtnI1OqEpMGRiBDDUG vQMrYQ5ib3RAU6IIZDAxTE6Au5m9D6xEAOQWBkEGqBIGpuQJCEPAFi0WAHkKogRkEc8FOQVFSAioHIQ4VxscLky7gRYpaAOVOB83ZA >png;base64,iVBORw0KGgoAAAAANSUhEUgAAADAAAAAQCAMAAABncAyDAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA и bQS4qAAAAEHRSTlMAMRDQiiHowAFBoWFRoLFx3eb7ogAAAMZJREFUKM+1UksSwyAIVUHAX+T+p602mTYkdqZd1AUL5f k+4NzfjiQvv/QXwkz++ /6kyblOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSDCDqDtDhO3ASgOypGJbMyVh4A3A8bBpQq1URM1exAEcTUHaF4R5ZzFQXDE+FuDIfET4AiqZFe+PykiQH YIbb8rAgTsAM3lvTjvc5DCVeORANFjSxbhfOqn6ux5wPICRojOf2f J81Uscj+bmEUc5q4jKCXucmPQAaYQaRCPmIUQAAAABJRU5ErkJggg==" /> и при .
д) Ако 0" png;base64,iVBORw0KGgoAAAANSUhEUgAAADkAAAATBAMAAADYAbjmAAAAJ1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA+jSoGAAAADHRSTlMAvyhB56FpgBDQkFHg6FX2AAAAy0lEQVQoz2N gIA8wK+CRZPMKwSNtY8DmgSbEVARnijBwHEPXYRgEYzkyMBwEUl3i3V JI0sFQU4BSPgwMHEKcU1USENKmwhAXA2VlGBhYDRhPxBgwMMOlVaWRZNkYWASaGKwcEbpVvRGyDAw6QHM1ChGy6rOh9p 4B8XIMgARCVnUamALKHgHau0CGgRNJVlUY7t+jwDCROMKQjpA1hEoy7FFgO8TAwLnSMrAALos /> и 0" png; base64, iVBORw0KGgoAAAANSUhEUgAAADkAAAATCAMAAAAd8VXnAAAAOVBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADLcPMfAAAAEnRSTlMANYHQITEQwEGh4HGQYVHwsQGBXjDVAAA9klEQVQ4y72TyW7FIAxFLQYPDAn4/z+2OKSt8kJfpUgtCxbAsX2vDcA/rs6xPwJrKpLi A5 CVAfKObx9FF+6HLY0NNf8Sn+SV7TvZrmRSsZDDjcoPLF8Ogh5k0kEixe69xL2u8wrxReZBkpEWlBTFlAfmOxuEtn4l4SCrFd8Ah9FRuHlcsWlb5DQTT6vIAaSF3uD8JxknqSeZdRYpMmi6Z/ T1q9p+ktYbKdBG hO7nbXI3lbzopxyFo+4j7yTyVScTvXi26TCkqvXZF89eyJ0v8f0kALg9uzQ7aJMfTquGPd9zFRec1Z/rzf9AzFt58oGajuX+/IN/AGa9CaC3YPi9AAAAAAElFTkSuQm CC" style="vertical-align: middle;" />
Наистина имаме:
Правим заместване във втория интеграл. Когато се променя от до , переменната се променя от 1 до . Следователно смисъл,
Чрез метода на математическата индукция е възможно да се докаже валидността на равенството (1) за всяко крайно множествоположительных чисел
е) Ако 0" png;base64,iVBORw0KGgoAAAANSUhEUgAAADkAAAATBAMAAADYAbjmAAAAJ1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAB+jSoGAAAADHRSTlMAvyhB56FpgBDQkFHg6FX2AAAAy0lEQVQoz2Ng IA 8wK+CRZPMKwSNtY8DmgSbEVARnijBwHEPXYRgEYzkyMBwEUl3i3VJI0sFQU4BSPgwMHEKcU1USENKmwhAXA2VlGBhYDRhPxBgwMMOlVaWRZNkYWASaGKwcEbpVvRGyDAw6QHM1ChGy6rOh9p4B8 XIMgARCVn UamALKHgHau0CGgRNJVlUY7t+jwDCROMKQjpA1hEoy7FFgO8TAwLnSMrAALos /> и 0" png;base64,iVBORw0KGgoAAAANSUhEUgAAADkAAAATCAMAAAAd8VXnAAAAOVBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADLcPMfAAAAEnRSTlMANYHQITEQwEGh4HGQYVHwsQGBXjDVAAAA9klEQVQ4y72TyW7FIAxFLQYPDAn4/z+2OKSt8kJfpUgtCxbAsX2vDcA/rs6xPwJrKpLiA 5CVAfKObx9FF+6HLY0NN f8Sn+SV7TvZrmRSsZDDjcoPLF8Ogh5k0kEixe69xL2u8wrxReZBkpEWlBTFlAfmOxuEtn4l4SCrFd8Ah9FRuHlcsWlb5DQTT6vIAaSF3uD8JxknqSeZdRYpMmi6Z /T1q9p+ktYbKdBGhO7nbX I3lbzopxyFo+4j7yTyVScTvXi26TCkqvXZF89eyJ0v8f0kALg9uzQ7aJMfTquGPd9zFRec1Z/rzf9AzFt58oGajuX+/IN/AGa9CaC3YPi9AAAAAElFTkSuQ mCC" style="vertical-align: middle;" />, то се попълва равенството
В samouls деле, иimes равенства (1) следва, чисионо откуда бе201 тру advance поорсеается треуемое равенство (3).
ж) Ако 0" png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAQCAMAAABncAyDAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADbQS4qAAAAEHRSTlMAMRDQiiHowAFBoWFRoLFx3eb7ogAAAMZJ REFUK M+1UksSwyAIVUHAX+T+p602mTYkdqZd1AUL5fk+4NzfjiQvv/QXwkz++/6kybloOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSDCDqDtDhO3ASgOypGJbMyVh4A3A8bBpQq1URM1ex AEcTUHaF4 R5ZzFQXDE+FuDIfET4AiqZFe+PykiQHYIbb8rAgTsAM3lvTjvc5DCVeORANFjSxbhfOqn6ux5wPICRojOf2fJ81Uscj+bmEUc5q4jKCXucmPQAaYQaRCPmIUQAAAABJRU5ErkJggg==" /> и — натуральное число, то
Това лесно следва от равенства (2).
з) Логарифмическата функция се стреми към , когато , и к , когато
Например размер размер 1" png;base64,iVBORw0KGgoAAAANSUhEUgaAAAC4AAAATBAMAAAAdcyJ3AAAAKlBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHrpZrAAAADXRSTlMAAcEnpULlgRHQUZFiJ/hrwwAAAKlJREFUGNNjYCAB MGMXFnUSwCbMnnIJSXx5A5wpiCzOM9sAxmQEi3MU7SgG8aRUDJDFGc0Kl92AWKcSgCTOkcTANhHCZ3UKRIiz32 LodYC528kALi6WyLD2AEzccwFcvFeRYa8BTDmSObIbGKZBnCuqhGwvpwP3FY itcHcK3hQEas5WugP21xSYMPvdu3eBOoWlL6OHg6AgiOJMxBqqjLaOWMVZlJSwiAIAYEImbANLL8IAAAAASUVORK5CYII =" style="vertical-align: middle;" />. Тогава Колкото 0" PNG;BASE64,Ivborw0KGGOOAAaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaadnrstlmac/ m0fd6re+Ithrbfl4aaaSsstrbfl4aaaSsstrbfl4aaaSstrabvcj PY2AgcNyQceCW5IgCeM11EFSY22OAst3cktheMFGIYFGYFGYFGYFGWXCVGUCFFFIKNQGDNAPIkmpkjwXMWXMWOKIvayaki /> При 1" P ng;Bace64,Ivborw0KGGOOAAC4Atbamaaadcyj3 Cellation of 2017 10th Annual 'Start of the Year' Aside, '1000-те най-добри неща, които никога не сте знаели за 100-те най-добри неща, които никога не сте знаели за 100-те най-добри неща, които никога не сте знаели за себе си 3 Imbanll8iaaaaSacy5cyii=" style="ver tical-align: middle;" />, то
Ако искате, можете да получите снежинка от снежинка Не се страхувайте, и защото Так как
Премахнете снежинките снежинки и снежинките (5) снежинки, моля, нейните стойности влизат в множество всички действителни чисел. Ако искате, можете да получите усмивка на лицето си, можете да получите усмивка на лицето си хубаво. Публикувайте това значение буквой е. Не на последно място, малко по-евтини снежинки
и) Справедливо равество На земята, от другата страна на монетатание имаме:
Следователно, и , това е, .
В конструкцията на теорията на логаритмичната функция, описана по-горе, ние дефинираме експоненциалната функция като обратна на логаритмичната функция (съществуването на обратната функция следва от факта, че функцията е строго нарастваща и непрекъсната на интервала. Свойствата на експоненциалната функция се извличат от съответните свойства на логаритмичната функция.
Накрая дефинираме степента с произволен експонент, като 0\двоеточие
x^= e^>"png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ0AAAAVCAMAAABrGxxRAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADbQS4qAAAAAEHRSTlMAwNWhQBBbgSkGQbCR8HFwXXAC 4AA AAfNJREFUSMftle2SqyAMhgkhHwuo3P/VnoC61RZd/LdnZpmxM62UPCTvmzj3t/7rlUr4zXh/dMr8aPuiLzoKi2Om9StxINaHwQPdvp9RJbll9DhcNMm23eikoC6wwol64OkB2pd6F H+XG/ YtTB48MKNzYYr8XVl7QllPIgcz5wd0NIllr8TrHV7qB4wWpBgXFXzpzsg2uvrD9THYeTW3/T79oGyQQbgVZHfDmU4pWFmv+BQhfrak+gnlJneWjDiNipkmE/FSVDt0IBnMYnteIKmmp Ee+d4n5 9kespV2OrygDEtvjNKMww4+uIIGaYU5ZdEntLAQICVIAaLURZMz7Ocgum148nvL3ZoHS6MToYjkkkCzL4FGnuVOCeFjfdmfbSj6O6p2lRmUu8n5HP1OHjtLBTRJrQq0dfLr5i+W w9sLEFmacrl4 LTYWxUwMvn3TnqzWfOhpunVA4mhAeNdq+F2l+0U2bKz7voEUedPTiRR6OgW6Ac2Vho/scF3zVBHuVjSU/InMCNNcA5y737oqt39V5EPXU8bFyQ2fIhYMp9iFIax7GlVAm8hZaw d11lOZKreLXg 2e1ANWaj48dqGF0eKK4nIARMNFtN7ZGmxdfIaglcBds9tGnNF4u8iAeHwhPjYuOlUldIRH31KzueuZc8MXxvf8AU2MQynjIaCsAAAAASUVORK5CYII=" />.
От свойствата на логаритмичните и експоненциалните функции следва, че при 0 "png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAQCAMAAABncAyDAAAAM1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADbQS4qAAAAAEHRSTlMAMRDQiiHowAFBoWFRoLFx3eb7ogAAAMZJREFUKM+1UksSwyAIV UHAX+T+p602mTYkdqZd1AUL5fk+4NzfjiQvv/QXwkz++/6kyblOYfXmMd4vNxglaF//xu0KEeJZdVYXkDFUbhaSDCDqDtDhO3ASgOypGJbMyVh4A3A8bBpQq1URM1exAEcTUHaF4R5ZzFQXDE +FuDIfET4AiqZFe+PykiQHYIbb8rAgTsAM3lvTjvc5DCVeORANFjSxbhfOqn6ux5wPICRojOf2fJ81Uscj+bmEUc5q4jKCXucmPQAaYQaRCPmIUQAAAABJRU5ErkJggg==" /> and we have:
Ето защо . Това показва, че това определение за степен съвпада с обичайното.