sqrt[2]{sqrt[3]{64}}=2^n/m eching

$$\sqrt[ 2 ] { \sqrt[ 3 ] { 64 } } = 2 ^ { n / m }$$

n uchun yechish

$$n=m$$

$$m\neq 0$$

Logaritm ifodasidan foydalanish qadamlari

\sqrt[3]{64} ni hisoblab, 4 natijasiga ega bo‘ling.

$$\sqrt[2]{4}=2^{\frac{n}{m}}$$

\sqrt[2]{4} ni hisoblab, 2 natijasiga ega bo‘ling.

$$2=2^{\frac{n}{m}}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2^{\frac{n}{m}}=2$$

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{\frac{1}{m}n}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{\frac{1}{m}n})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

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

Ikki tarafini \log(2) ga bo‘ling.

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

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

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

Ikki tarafini m^{-1} ga bo‘ling.

$$n=\frac{m}{1}$$

m uchun yechish

$$m=n$$

$$n\neq 0$$