Question

tìm soos nguyên x nếu biết

1/ 5.3\(^x\)= 5.3\(^4\)

2/ 9.5\(^x\)= 6.5\(^6\)+3.5\(^6\)

3 /2.3\(^{x+2}\)+ 4.3\(^{x+1}\)=10.3\(^6\)

Answer 1

1;Ta có\(5.3^x=5.3^4\)

\(\Rightarrow3^x=3^4\)

\(\Rightarrow x=4\)

2.Ta có \(9.5^x=6.5^6+3.5^6\)

\(\Rightarrow9.5^x=5^6.\left(6+3\right)\)

\(\Rightarrow9.5^x=9.5^6\)

\(\Rightarrow5^x=5^6\)\

\(\Rightarrow x=6\)

3, Ta có \(2.3^{x+2}+4.3^{x+1}=10.3^6\)

\(\Rightarrow3^{x+1}.\left(2.3+4\right)=10.3^6\)

\(\Rightarrow3^{x+1}.10=10.3^6\)

\(\Rightarrow3^{x+1}=3^6\)

\(\Rightarrow x+1=6\)

\(\Rightarrow x=5\)

Answer 2

a) 5.3^x = 5.3⁴

=> 3^x=3⁴

=> x=4

b) 9.5^x=6.5⁶+3.5⁶

=> 9.5^x = (6+3)5⁶

=> 9.5^x=9.5⁶

=> 5^x=5⁶

=> x=6

c) 2.3^x+2 + 4.3^x+1 = 10.3⁶

=> 2.3^x+1.3 + 4.3^x+1 = 10.3⁶ 

=> 6.3^x+1+4.3^x+1=10.3⁶

=> (6+4).3^x+1=10.3⁶

=> 10.3^x+1=10.3⁶

=> 3^x+1=3⁶

=> x+1=6

=> x=5