log10-log0.01+log100-log_{36}6+lne eching

$$\log 10 - \log 0.01 + \log 100 - \log _ { 36 } 6 + \ln e$$

Baholash

$$5,5$$

Yechim qadamlari

Logarifm 10 asosga ko‘ra 10 1 ga teng.

$$1-\log_{10}\left(0,01\right)+\log_{10}\left(100\right)-\log_{36}\left(6\right)+\log_{e}\left(e\right)$$

Logarifm 10 asosga ko‘ra 0,01 -2 ga teng.

$$1-\left(-2\right)+\log_{10}\left(100\right)-\log_{36}\left(6\right)+\log_{e}\left(e\right)$$

-2 ning teskarisi 2 ga teng.

$$1+2+\log_{10}\left(100\right)-\log_{36}\left(6\right)+\log_{e}\left(e\right)$$

3 olish uchun 1 va 2'ni qo'shing.

$$3+\log_{10}\left(100\right)-\log_{36}\left(6\right)+\log_{e}\left(e\right)$$

Logarifm 10 asosga ko‘ra 100 2 ga teng.

$$3+2-\log_{36}\left(6\right)+\log_{e}\left(e\right)$$

5 olish uchun 3 va 2'ni qo'shing.

$$5-\log_{36}\left(6\right)+\log_{e}\left(e\right)$$

Logarifm 36 asosga ko‘ra 6 \frac{1}{2} ga teng.

$$5-\frac{1}{2}+\log_{e}\left(e\right)$$

\frac{9}{2} olish uchun 5 dan \frac{1}{2} ni ayirish.

$$\frac{9}{2}+\log_{e}\left(e\right)$$

Logarifm e asosga ko‘ra e 1 ga teng.

$$\frac{9}{2}+1$$

\frac{11}{2} olish uchun \frac{9}{2} va 1'ni qo'shing.

$$\frac{11}{2}$$

Omil

$$\frac{11}{2} = 5\frac{1}{2} = 5,5$$