1=2.5^n(frac{-268{10.85x})} eching

$$1 = 2.5 ^ { n ( \frac { - 268 } { 10.85 x } ) }$$

n uchun yechish

$$n=0$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2,5^{n\times \frac{-268}{10,85x}}=1$$

Shartlarni qayta saralash.

$$2,5^{\left(-\frac{268}{10,85x}\right)n}=1$$

Shartlarni qayta saralash.

$$2,5^{-\frac{268}{10,85x}n}=1$$

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2,5^{\left(-\frac{5360}{217x}\right)n}=1$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2,5^{\left(-\frac{5360}{217x}\right)n})=\log(1)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(-\frac{5360}{217x}\right)n\log(2,5)=\log(1)$$

Ikki tarafini \log(2,5) ga bo‘ling.

$$\left(-\frac{5360}{217x}\right)n=\frac{\log(1)}{\log(2,5)}$$

Asosiy tenglamani almashtirish orqali \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$\left(-\frac{5360}{217x}\right)n=\log_{2,5}\left(1\right)$$

Ikki tarafini -\frac{5360}{217}x^{-1} ga bo‘ling.

$$n=\frac{0}{-\frac{5360}{217x}}$$

n uchun yechish (complex solution)

$$n=\frac{i\times 2\times 217\pi n_{1}x}{5360\ln(2)-5360\ln(5)}$$

$$n_{1}\in \mathrm{Z}$$

$$x\neq 0$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}\\x\neq 0\text{, }&\text{unconditionally}\\x=-\frac{i\times \frac{5360\ln(2)-5360\ln(5)}{217}n}{2\pi n_{1}}\text{, }n_{1}\in \mathrm{Z}\text{, }n_{1}\neq 0\text{, }&n\neq 0\end{matrix}\right,$$

x uchun yechish

$$x\neq 0$$