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

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 = 7Then 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]