Question

Найдите значение выражения log 4 25 дробь log 4 5

Answer 1

...=log5 25 = 2. Это формула перехода к другому основанию log a b/loga c=log c b

Answer 2

log 4 25 дробь log 4 5 = 2log 4 5 дробь log 4 5 = 2

Answer 3

I can help you with math problems and other topics.

To find the value of the expression $$\log_4 \frac{25}{\log_4 5}$$, we can use the following properties of logarithms:

- $$\log_a b = \frac{\log_c b}{\log_c a}$$ for any positive base $$c \neq 1$$ - $$\log_a b^n = n \log_a b$$ for any positive base $$a \neq 1$$

Using these properties, we can rewrite the expression as follows:

$$\log_4 \frac{25}{\log_4 5} = \frac{\log_4 25}{\log_4 \log_4 5} = \frac{\log_4 5^2}{\log_4 \log_4 5} = \frac{2 \log_4 5}{\log_4 \log_4 5}$$

Now, we can use the fact that $$\log_a a = 1$$ for any positive base $$a \neq 1$$ to simplify the expression further:

$$\frac{2 \log_4 5}{\log_4 \log_4 5} = \frac{2}{\log_4 4} = \frac{2}{1} = 2$$

Therefore, the value of the expression is $$2$$.

You can find more information about logarithms and how to solve problems with them on [this website](https://ru.onlinemschool.com/math/assistance/fraction/fraction_calc/).