Question

Va rog dau coroana ajutatima

Answer 1

$a).9^{2x}=81^4 \\ 9^{2x}=(9^2)^4 \\ 9^{2x}=9^8 \\ 2x=8 \\ x=8:2 \\ x=4 \\ b).8^{3x}=64^3 \\ 8^{3x}=(8^2)^3 \\ 8^{3x}=8^6 \\ 3x=6 \\ x=6:3 \\ x=2$
$c).2^x+2^{x+1}+2^{x+2}=56 \\ 2^x(1+2^1+2^2)=56 \\ 2^x(1+2+4)=56 \\ 2^x(3+4)=56 \\ 2^x \cdot 7=56 \\ 2^x=56:7 \\ 2^x=8 \\ 2^x=2^3 \\ x=3$
$d).3^{x+2}+3^x=270 \\ 3^x(3^2+1)=270 \\ 3^x(9+1)=270 \\ 3^x \cdot 10=270 \\ 3^x=270:10 \\ 3^x=27 \\ 3^x=3^3 \\ x=3$
$e).3 \cdot 2^{x+2}-5 \cdot 2^{x+1}-2^x=2 \\ 2^x(3 \cdot 2^2-5 \cdot 2^1-1)=2 \\ 2^x(3 \cdot 4-5 \cdot 2-1)=2 \\ 2^x(12-10-1)=2 \\ 2^x(2-1)=2 \\ 2^x \cdot 1=2 \\ 2^x=2 \\ x=1$
$f).5^{x+2}-2 \cdot 5^{x+1}-12 \cdot 5^x=375 \\ 5^x(5^2-2 \cdot 5^1-12 \cdot 1) =375 \\ 5^x(25-10-12)=375 \\ 5^x(15-12)=375 \\ 5^x \cdot3=375 \\ 5^x=375:3 \\ 5^x=125 \\ 5^x=5^3 \\ x=3$
$g).2^x \cdot 3^{x+1}=108 \\ 2^x \cdot 3^x \cdot 3^1=108 \\ 2^x \cdot 3^x \cdot 3=108 \\ 2^x \cdot 3^x=108:3 \\ 2^x \cdot 3^x=36 \\ (2 \cdot 3)^x=36 \\ 6^x=36 \\ 6^x=6^2 \\ x=2$
$h).3^{x+1} \cdot 5^x=675 \\ 3^x \cdot 3^1 \cdot 5^x=675 \\ 3^x \cdot 3 \cdot 5^x=675 \\ 3^x \cdot 5^x=675:3 \\ 3^x \cdot 5^x=225 \\ (3 \cdot5)^x=225 \\ 15^x=225 \\ 15^x=15^2 \\ x=2$