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What is the smallest positive integer that will make x^x > 500,000? What
is the largest negative integer that will make x^(-x) > 500,000?

Respuesta :

luisejr77

Answer:

For    [tex]x^x > 500,000[/tex]  [tex]x=7[/tex]

For  [tex]x^{(-x)} > 500,000[/tex]  [tex]x=-7[/tex]

Step-by-step explanation:

We need to find the smallest positive whole number that satisfies the inequality:

[tex]x^x > 500,000[/tex]

We tested with x = 6

[tex]6^6=46,656\\\\46,656 > 500,000[/tex]

Inequality is not met because  [tex]46,656 < 500,000[/tex]

We test with the following integer x = 7

Then we have that:

[tex]7^7=823,543\\\\823,543 > 500,000[/tex]

Then the smallest positive integer that will make  [tex]x^x > 500,000[/tex]  is 7 because Inequality is met.

In the same way the largest negative integer that will make  [tex]x^{(-x)} >500000[/tex] is [tex]x=-7[/tex] Beacuse   [tex]7^{-(-7)}=823,543>500,000[/tex]

Answer:

Smallest positive integer value for [tex]x^x>500000[/tex] is,

x = 7,

Largest negative integer value for [tex]x^{-x}>500000[/tex] is,

x = -8

Step-by-step explanation:

If [tex]x^x>500000[/tex]

By graphing calculator,

[tex]x>6.83[/tex]

Thus, the smallest possible positive integer value of x is 7,

Now,

[tex]x^{-x}>500000[/tex]

Possible negative integer values of x are -6, -7 and -8,

If x = -6, -7, and -8,

[tex](-6)^{6}=46656[/tex]

[tex](-7)^{7}=-823543[/tex]

[tex](-8)^{8}=16777216[/tex]

[tex]\because 16777216 > 500000[/tex]

Thus, the largest negative integer value of the inequality [tex]x^{-x}>500000[/tex] is,

x = -8.

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