10(10^-5)-log_{10}(1000)*log_{10}(5^2*4) eching

$$10 ( 10 ^ { - 5 } ) - \log _ { 10 } ( 1000 ) * \log _ { 10 } ( 5 ^ { 2 } * 4 )$$

Baholash

$$-\frac{59999}{10000}=-5,9999$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va -5 ni qo‘shib, -4 ni oling.

$$10^{-4}-\log_{10}\left(1000\right)\log_{10}\left(5^{2}\times 4\right)$$

-4 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{10000} ni qiymatni oling.

$$\frac{1}{10000}-\log_{10}\left(1000\right)\log_{10}\left(5^{2}\times 4\right)$$

Logarifm 10 asosga ko‘ra 1000 3 ga teng.

$$\frac{1}{10000}-3\log_{10}\left(5^{2}\times 4\right)$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{1}{10000}-3\log_{10}\left(25\times 4\right)$$

100 hosil qilish uchun 25 va 4 ni ko'paytirish.

$$\frac{1}{10000}-3\log_{10}\left(100\right)$$

Logarifm 10 asosga ko‘ra 100 2 ga teng.

$$\frac{1}{10000}-3\times 2$$

6 hosil qilish uchun 3 va 2 ni ko'paytirish.

$$\frac{1}{10000}-6$$

-\frac{59999}{10000} olish uchun \frac{1}{10000} dan 6 ni ayirish.

$$-\frac{59999}{10000}$$

Omil

$$-\frac{59999}{10000} = -5\frac{9999}{10000} = -5,9999$$