140(1/2)^frac{t{n}}=40 eching

$$140 ( \frac { 1 } { 2 } ) ^ { \frac { t } { n } } = 40$$

t uchun yechish

$$t=\left(\log_{2}\left(7\right)-1\right)n$$

$$n\neq 0$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$140\times \left(\frac{1}{2}\right)^{\frac{1}{n}t}=40$$

Ikki tarafini 140 ga bo‘ling.

$$\left(\frac{1}{2}\right)^{\frac{1}{n}t}=\frac{2}{7}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{1}{2}\right)^{\frac{1}{n}t})=\log(\frac{2}{7})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\frac{1}{n}t\log(\frac{1}{2})=\log(\frac{2}{7})$$

Ikki tarafini \log(\frac{1}{2}) ga bo‘ling.

$$\frac{1}{n}t=\frac{\log(\frac{2}{7})}{\log(\frac{1}{2})}$$

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

$$\frac{1}{n}t=\log_{\frac{1}{2}}\left(\frac{2}{7}\right)$$

Ikki tarafini n^{-1} ga bo‘ling.

$$t=\frac{\left(-\left(-\log_{2}\left(7\right)+1\right)\right)n}{1}$$

n uchun yechish

$$n=-\log_{\frac{2}{7}}\left(2\right)t$$

$$t\neq 0$$