Question

Докажите что 48^25 < 344^17

Answer 1

представим в виде  

число А 48^25=2^3^25*6^25=2^3^25*216^3  

число Б 344^17=2^3^17*43^17=2^3^17*43^17  

видно что 2^3^25 больше чем 2^3^17 а 216^23 больше чем 43^17:отсюда А больше Б

Answer 2

To prove that $48^{25} < 344^{17}$, we can take the $17$th root of both sides to simplify the comparison. Taking the $17$th root preserves the inequality because $17$ is an odd number, and for positive numbers, taking the $17$th root is a monotonically increasing operation.

So, let's take the $17$th root of both sides:

$\sqrt[17]{48^{25}} < \sqrt[17]{344^{17}}$

Now, simplify both sides:

$48^{\frac{25}{17}} < 344^{\frac{17}{17}}$

$48^{\frac{25}{17}} < 344$

To compare the two values, let's calculate $48^{\frac{25}{17}}$:

$48^{\frac{25}{17}} \approx 1812.168$

Since $48^{\frac{25}{17}}$ is approximately $1812.168$ and $344$ is greater than $1812.168$, the inequality holds:

$48^{\frac{25}{17}} < 344$

Therefore, the original inequality $48^{25} < 344^{17}$ is true.