x-log(x+1)=0 (уравнение)

Найду корень уравнения: x-log(x+1)=0

Вы ввели

x - log(x + 1) = 0

$$x - \log{\left(x + 1 \right)} = 0$$

Подробное решение

Дано уравнение
$$x - \log{\left (x + 1 \right )} = 0$$
преобразуем
$$x - \log{\left (x + 1 \right )} = 0$$
$$x - \log{\left (x + 1 \right )} = 0$$
Сделаем замену
$$w = \log{\left (x + 1 \right )}$$
Приводим подобные слагаемые в левой части ур-ния:

x - w = 0

Разделим обе части ур-ния на (x - w)/w

w = 0 / ((x - w)/w)

Получим ответ: w = x
делаем обратную замену
$$\log{\left (x + 1 \right )} = w$$
Дано уравнение
$$\log{\left (x + 1 \right )} = w$$
$$\log{\left (x + 1 \right )} = w$$
Это уравнение вида:

log(v)=p

По определению log

v=e^p

тогда

         w
         -
         1
x + 1 = e 

упрощаем
$$x + 1 = e^{w}$$
$$x = e^{w} - 1$$
подставляем w:

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

Сумма и произведение корней

сумма

0 + 0

$$0 + 0$$

=

0

$$0$$

произведение

1*0

$$1 \cdot 0$$

=

0

$$0$$

Численный ответ

x1 = 1.02290048631435e-6

x2 = 1.15655685932572e-6 + 3.56628029901262e-7*i

x3 = 1.15997586421077e-6 + 3.5084708321914e-7*i

x4 = 1.19711765366761e-6 + 2.90579755808275e-7*i

x5 = 9.37823627309638e-7

x6 = 9.27996674275468e-7

x7 = 1.04442879382009e-6

x8 = 1.14002615739782e-6 + 3.85002507928671e-7*i

x9 = 1.20272528988125e-6 + 2.81972171837316e-7*i

x10 = 1.20001159645375e-6 + 2.86118853240951e-7*i

x11 = 1.01261302245021e-6 + 6.16961436562624e-7*i

x12 = 1.0378150063821e-6

x13 = 1.12934054686334e-6 + 4.03668022727684e-7*i

x14 = 7.59259996457659e-7

x15 = 1.18709327086388e-6 + 3.06323899588451e-7*i

x16 = 1.12311706832162e-6 + 4.14639183706388e-7*i

x17 = 1.07374958864977e-6

x18 = 1.06167865493264e-6

x19 = 1.11613681771521e-6 + 4.27022920742237e-7*i

x20 = 1.10821806090801e-6 + 4.4116307742805e-7*i

x21 = 1.05630935654691e-6

x22 = 8.92198822732336e-7

x23 = 9.17237166826894e-7

x24 = 1.19238588460948e-6 + 2.97956598461101e-7*i

x25 = 8.41420712545984e-7

x26 = 1.13494252568346e-6 + 3.9385396003434e-7*i

x27 = 1.03066628829242e-6

x28 = 1.16317634247958e-6 + 3.45465940600223e-7*i

x29 = 1.16901459685099e-6 + 3.35729780483775e-7*i

x30 = 9.5518970223767e-7

x31 = 1.18318773101605e-6 + 3.12572643430917e-7*i

x32 = 8.98407189038537e-7 + 8.32685882697166e-7*i

x33 = 1.05903702219829e-6

x34 = 1.1446717296618e-6 + 3.76962530688077e-7*i

x35 = 1.08845093052897e-6 + 4.76826036195802e-7*i

x36 = 1.06913279142964e-6

x37 = 1.19068987632594e-6 + 3.00624874602471e-7*i

x38 = 6.61256122479308e-7

x39 = 1.15289065177433e-6 + 3.62862372742944e-7*i

x40 = 1.01875536538395e-6

x41 = 1.17422484320244e-6 + 3.2713412983614e-7*i

x42 = 1.1766310886538e-6 + 3.23195937043171e-7*i

x43 = 1.04755661008497e-6

x44 = 1.20402086749493e-6 + 2.80005181346823e-7*i

x45 = 1.17169037282661e-6 + 3.31303984427381e-7*i

x46 = 9.89136070354524e-7

x47 = 8.18938530915917e-7

x48 = 1.19401986277083e-6 + 2.95397841838197e-7*i

x49 = 1.19858853280392e-6 + 2.88307523823124e-7*i

x50 = 5.7893623615318e-7

x51 = 0.0

x52 = 9.70131088110912e-7

x53 = 1.20650041586716e-6 + 2.76264107271187e-7*i

x54 = 1.2052785714157e-6 + 2.78103706941556e-7*i

x55 = 1.07811616799684e-6

x56 = 1.06672234487578e-6

x57 = 1.14894284241796e-6 + 3.69614488686334e-7*i

x58 = 1.05057497641124e-6

x59 = 9.71823919026363e-7 + 6.93662087029048e-7*i

x60 = 1.0759626276941e-6

x61 = 7.17441241527563e-7

x62 = 1.07147405064123e-6

x63 = 1.18110312567554e-6 + 3.15932594895975e-7*i

x64 = 1.00986581987569e-6

x65 = 6.63586964275395e-7 + 1.27323078562302e-6*i

x66 = 1.18518213374936e-6 + 3.0937400717924e-7*i

x67 = 9.05376512895595e-7

x68 = 4.37089644970953e-7

x69 = 1.01441606596874e-6

x70 = 1.00005426162008e-6

x71 = 1.04118425475141e-6

x72 = 1.21106446769688e-6 + 2.69460864741462e-7*i

x73 = 9.83189061760235e-7

x74 = 1.09910946628884e-6 + 4.57536095565927e-7*i

x75 = 1.08021300727928e-6

x76 = 1.18892733523594e-6 + 3.03410921969358e-7*i

x77 = 1.20138965607207e-6 + 2.84008630102398e-7*i

x78 = 1.20884383920049e-6 + 2.72757337298567e-7*i

x79 = 9.76868622801243e-7

x80 = 1.06001111002171e-6 + 5.28868743377344e-7*i

x81 = 1.05349053286303e-6

x82 = 9.62925091903436e-7

x83 = 9.46851965705798e-7

x84 = 1.06423897633676e-6

x85 = 1.21317381645682e-6 + 2.66354017149206e-7*i

x86 = 1.07570315930708e-6 + 5.00059657967668e-7*i

x87 = 1.1955958860525e-6 + 2.92941147362249e-7*i

x88 = 1.02686635027801e-6

x89 = 1.03431225465055e-6

x90 = 1.0050857032895e-6

x91 = 8.60668995725532e-7

x92 = 1.03991142497353e-6 + 5.6605266091366e-7*i

x93 = 1.21213239430586e-6 + 2.67884916214006e-7*i

x94 = 1.17892051580713e-6 + 3.19468262786485e-7*i

x95 = 8.77422058608653e-7

x96 = 9.94747050586931e-7

x97 = 1.16618242613292e-6 + 3.40439564072992e-7*i

x98 = 1.2076882633439e-6 + 2.74483020524702e-7*i

x99 = 1.08225575820544e-6

x100 = 7.92125255839739e-7

x101 = 1.20996874454959e-6 + 2.7108417662621e-7*i

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