Question

Решить неравенство (1 1/5)^x>5/6​

Answer 1

Ответ:

x∈(-1;+∞)

Объяснение:

(6/5)^x>5/6

(6/5)^x>(6/5)^-1

x>-1

Answer 2

To solve the inequality $(1 + \frac{1}{5})^x > \frac{5}{6}$, we first need to simplify the left-hand side:

$(1 + \frac{1}{5})^x = \frac{6}{5}^x$

Now, the inequality becomes:

$\frac{6}{5}^x > \frac{5}{6}$

To solve this inequality, we can take the logarithm of both sides. We can use either the natural logarithm (base $e$) or the common logarithm (base 10). Let's use the natural logarithm:

$\ln\left(\frac{6}{5}^x\right) > \ln\left(\frac{5}{6}\right)$

Now, we can use the property of logarithms that $\ln(a^b) = b \cdot \ln(a)$:

$x \cdot \ln\left(\frac{6}{5}\right) > \ln\left(\frac{5}{6}\right)$

Now, isolate $x$ by dividing both sides by $\ln\left(\frac{6}{5}\right)$:

$x > \frac{\ln\left(\frac{5}{6}\right)}{\ln\left(\frac{6}{5}\right)}$

Now, we can use a calculator to compute the right-hand side of the inequality:

$x > \frac{\ln\left(\frac{5}{6}\right)}{\ln\left(\frac{6}{5}\right)} \approx -1.5696$

So, the solution to the inequality is $x > -1.5696$.