Question

who is greater among the number 39^(40) and 40^(39)

Answer 1

Answer:

Answer is 39^40

Step-by-step explanation:

39^40 is greater than 40^39

Answer 2

Answer:

39^(40) is greater than 40^(39)

Let us just compare the two numbers.

The L.C.M of 39 and 40 is 1560. So we just do the 1560th root operation on both of them

now \sqrt[1560]{39^{40} } =39^{\frac{1}{39} }

1560

39

40

=39

39

1

and \sqrt[1560]{40^{39} } =40^{\frac{1}{40} }

1560

40

39

=40

40

1

We know that the function f(x) = x^{\frac{1}{x} }x

x

1

is a decreasing function whenever x>=e

so f(40) < f(39) or f(39) > f(40)

notice that f(39) = 39^{\frac{1}{39} }39

39

1

and f(40) = 40^{\frac{1}{40} }40

40

1

so 39^{\frac{1}{39} }39

39

1

> 40^{\frac{1}{40} }40

40

1

now raising 1560th power on both sides we get 39^(40) > 40^(39)