Question

Tìm số nguyên x biết 5^x.5^x+1.5^x+2<\(\frac{10^{18}}{2^{18}}\)

Answer 1

\(\frac{10^{18}}{2^{18}}=\frac{\left(2.5\right)^{18}}{2^{18}}=\frac{2^{18}.5^{18}}{2^{18}}=5^{18}\)

vậy 5^x.5^x+1.5^x+2=5^{x+(x+1)+(x+2)}<5¹⁸=>x+(x+1)+(x+2) <18

vậy 3x+3<18 thì3x<15 =>x<5 

x <5 vay65 x thuộc 1;2;3;4

vậy x=1;2;3;4

Answer 2

X=1;2;3;4

Answer 3

\(\frac{10^{18}}{2^{18}}=\frac{\left(2.5\right)^{18}}{2^{18}}=\frac{2^{18}.5^{18}}{2^{18}}=5^{18}\)

Vậy 5^x.5^x+1.5^x+2=5^{x+(x+1)-(x+2)}<5¹⁸

=> x+(x+1)-(x+2)<18

Vậy 3x+3<18 thì 3x<15 

=> x<5

Vậy x={ 1;2;3;4}