Question

determine o conjunto solução das seguintes equações exponenciais

Answer 1

$a)\\5^{x+1}+5^{x+2}=30\\\\5^x(5^1+5^2)=30\\\\5^x.(5+25)=30\\\\5^x\;.\;30=30\\\\5^x=1\\\\5^x=5^0\\\\x=0$

$b)\\2^{x-1}+2^{x+2}=36\\\\2^x(2^{-1}+2^2)=36\\\\2^x(\frac{1}{2}+4)=36\\\\2^x(\frac{9}{2})=36\\\\2^x=36.\frac{2}{9}\\\\2^x=\frac{72}{9}\\\\2^x=8\\\\2^x=2^3\\\\x=3$

$c\\3^{x+1}+3^{x+2}=12\\\\3^x(3^1+3^2)=12\\\\3^x(12)=12\\\\3^x=1\\\\3^x=3^0\\\\x=0$

$d\\2^{x+1}+2^{x+3}=20\\\\2^x(2^1+2^3)=20\\\\2^x(10)=20\\\\2^x=2\\\\2^x=2^1\\\\x=1$