MATH SOLVE

2 months ago

Q:
# 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?

Accepted Solution

A:

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]