Question

n to the power 200 is less than 5 to the power 300.find the largest integer n that satisfies the equation.

Answer 1

ie 25 because
5to the power 300=
5to the power 3×100 ie
125to the power 100
25 to the power 2×100 is answer

Answer 2

Answer:

n = 11 will satisfy n²⁰⁰ < 5³⁰⁰

Step-by-step explanation:

Given that n²⁰⁰ < 5³⁰⁰

We know that (xᵃ)ᵇ = xᵃᵇ

Therefore, using this property, we get

(n²)¹⁰⁰ < (5³)¹⁰⁰

Raising both the sides to the power 1/100

We know that $(x^{a})^{\frac{1}{a}}$ = x

Therefore, using this property,

=> n² < 5³

=> n² < 125

Taking square root both side, we get

=> n < $\sqrt{125}$

=> n < 11.18

Therefore, the largest integer n < 11.18 is 11

Therefore, n = 11 will satisfy n²⁰⁰ < 5³⁰⁰