Question

Сравнитьlog1/3 (2/3) и log1/3 (5/6) Подробно пожалуйста ​

Answer 1

Ответ: первый (слева) логарифм больше, т.к. 2/3 < 5/6

Объяснение.

Answer 2

I can help you with your math question. To compare $$\log_{1/3}(2/3)$$ and $$\log_{1/3}(5/6)$$, we need to use the properties of logarithms. First, we can rewrite the logarithms as exponents using the definition of logarithm:

$$\log_{1/3}(2/3) = x \iff (1/3)^x = 2/3$$ $$\log_{1/3}(5/6) = y \iff (1/3)^y = 5/6$$

Next, we can use the property of exponentiation that says $$a^b = c \iff a^{-b} = 1/c$$ to rewrite the equations as:

$$(1/3)^{-x} = 3/2$$ $$(1/3)^{-y} = 6/5$$

Now, we can use the property of logarithms that says $$\log_a(b) = \log_c(b) / \log_c(a)$$ to convert the bases of the logarithms to a common base, such as 10:

$$-x = \log_{10}(3/2) / \log_{10}(1/3)$$ $$-y = \log_{10}(6/5) / \log_{10}(1/3)$$

Using a calculator, we can find the values of the logarithms:

$$-x \approx 0.6309 / -0.4771 \approx -1.3224$$ $$-y \approx 0.0792 / -0.4771 \approx -0.1660$$

Multiplying both sides by -1, we get:

$$x \approx 1.3224$$ $$y \approx 0.1660$$

Therefore, $$\log_{1/3}(2/3) > \log_{1/3}(5/6)$$ because $$x > y$$. I hope this helps you understand the comparison of logarithms.Ответь+подробно.++Сравнитьlog1/3+(2/3)+и+log1/3+(5/6)+Подробно+пожалуйста+​+

Answer 3

Для сравнения выражений `log1/3+(2/3)` и `log1/3+(5/6)`, мы можем использовать свойства логарифмов и математические операции. Давайте разберемся подробнее.

Выражение 1: log1/3+(2/3)

Для начала, давайте рассмотрим выражение `log1/3+(2/3)`.

Шаг 1: Применим свойство логарифма, которое гласит, что `log_a(b) + log_a(c) = log_a(b * c