Question

Va rog foarte frumos?

Answer 1

$a) 3^{x+2} + 3^{x} =270 \\ 3^{x} *3 ^{2} +3^{x}=270 \\ 3^{x}( 3^{2} +1)=270 \\ 3 ^{x} *10=270 \\ 3^{x}=27 \\ x=3 \\ b)3* 2^{x+2} -5* 2^{x+1} - 2^{x}=2 \\ 3* 2^{x}*2 ^{2} -5*2^{x}*2-2^{x}=2 \\ 2^{x}(3*4-5*2-1)=2 \\ 2^{x}*1=2 \\ 2^{x}=2 \\ x=1$

Answer 2

$f)3^{x+2} + 3^{x}=3 ^{3} *10 \\ \\ 3^{x} *3^{2} +3^{x} =3 ^{3} *10 \\ \\ 3^{x} (3^{2}+1)= 3 ^{3} *10 \\ \\3^{x} = \frac{3 ^{3} *10}{10} \\ \\ 3^{x} = 3^{3} \\ \\ x=3 \\ \\ g)3*2 ^{x}* 2^{2} -5*2^{x} *2-2^{x} =2 \\ 2^{x} (3* 2^{2} -5*2-1)=2 \\ \\ 2^{x} (12-10-1)=2 \\ \\ 2^{x} =2 ^{1} \\ x=1$