Numerical problems

Question

Arrange the following in ascending order 3 to the power 34, 2 to the power 51, 7 to the power 17. How? Also, please explain.

Answer 1

You have $7^{17}, (2^3)^{17}, (3^2)^{17}$

Answer 2

The exponents are all multiples of 17. Thus, we can order the following:

$7<2^3<3^2$

Raising each to the $17$th power, we obtain:

$7^{17} < 2^{51} < 3^{34}$.

The inequality is preserved, because $x\mapsto x^{17}$ is a strictly increasing function.

Answer 3

we have $7^{17}<2^{51}<3^{34}$