Question

решить уравнения$2 ^{x} +2 ^{x-3} =72 \\ 5 ^{x} +5 ^{x+2} =130$

Answer 1

1)
(2^3+1)*2^x-3=72
(8+1)*2^x-3=72
9*2^x-3=72
2^x-3=8
2^x-3=2^3
x-3=3
x=3+3
x=6
2)
(1+5^2)*5^x=130
(1+25)*5^x=130
26*5^x=130
5^x=5
5^x=5^1
x=1

Answer 2

2^x + 2^(x - 3 ) = 72 
2^x * ( 1 + ( 1/8 )) = 72 
2^x = 72 : ( 9/8 ) 
2^x = 64
2^x = 2^6
x = 6 
--------------------------------
5^x + 5^( x + 2 ) = 130 
5^x * ( 1 + 25 ) = 130 
5^x = 130 : 26 
5^x = 5 
x = 1