Question

resolvem isso que esta no print pfv

Answer 1

1)

$a)2 ^{x+3} = \frac{1}{8} \\ \\ 2 ^{x+3}=2 ^{-3} \\ \\ x+3=-3 \\ \\ x=-3-3 \\ \\ x=-6 \\ \\ \\ b)5 ^{3x+1} =25 \\ \\ 5 ^{3x+1}=5 ^{2} \\ \\ 3x+1=2 \\ \\ 3x=2-1 \\ \\ 3x=1 \\ \\ x= \frac{1}{3}$


$c)81^{x-2} = \sqrt[4]{27} \\ \\ 3 ^{4 (^{x-2}) }= \sqrt[4]{3 ^{3} } \\ \\ 3 ^{4x-8} =3 ^{ \frac{3}{4} } \\ \\ 4x-8= \frac{3}{4} \\ \\ 4x= \frac{3}{4}+8 \\ \\ \frac{16x}{4} = \frac{3+32}{4} \\ \\ 16x=35 \\ \\ x= \frac{35}{16}$


$d) \sqrt{4 ^{x+1} } = \sqrt[3]{16} \\ \\ \sqrt{4^{{x+1} } } = \sqrt[3]{4 ^{2} } \\ \\ 4 ^{ \frac{1}{2}(x+1)}=4 ^{ \frac{2}{3} } } \\ \\ \frac{1}{2} (x+1)= \frac{2}{3} \\ \\ \frac{x}{2} + \frac{1}{2} = \frac{2}{3} \\ \\ \frac{3x+3}{6} = \frac{4}{6} \\ \\ 3x+3=4 \\ \\ 3x=4-3 \\ \\ 3x=1 \\ \\ x= \frac{1}{3}$



$e) \sqrt{5 ^{x} } *25 ^{x+1} =(0,2) ^{1-x} \\ \\ 5 ^{ \frac{x}{2} } *5 ^{2(x+1)} =( \frac{2}{10} ) ^{1-x} \\ \\ 5 ^{ \frac{x}{2} } *5 ^{2x+2} =( \frac{1}{5} ) ^{1-x} \\ \\ 5 ^{ \frac{x}{2} } *5 ^{2x+2} =5 ^{-1} ^ {(1-x)} \\ \\ 5 ^{\frac{x}{2} } +^{2x+2}} =5 ^ {(-1+x)} \\ \\ \frac{x}{2} +2x+2=-1+x \\ \\ \frac{x}{2} +2x-x=-1-2 \\ \\ \frac{x}{2} +x=-3 \\ \\ \frac{x+2x}{2} = \frac{-6}{2} \\ \\ x+2x=-6 \\ \\ 3x=-6 \\ \\ x= -\frac{6}{3} \\ \\ x=-2$


2)

$a) log _{4} 32 \\ \\ 4 ^{x} =32 \\ \\ 2 ^{2x} =2 ^{5} \\ \\ 2x=5 \\ \\ x= \frac{5}{2} \\ \\ \\ \\ b)log _{100} 1000 \\ \\ 100 ^{x} =1000 \\ \\ 10 ^{2x} =10 ^{3} \\ \\ 2x=3 \\ \\ x= \frac{3}{2} \\ \\ \\ \\ c)log _{27} 3 \sqrt{9} \\ \\ 27 ^{x} =3 \sqrt{9} \\ \\ 3 ^{3x} =3* \sqrt{3 ^{2} } \\ \\ 3 ^{3x} =3*3 \\ \\ 3 ^{3x}=9 \\ \\ 3 ^{3x}=3 ^{2} \\ \\ 3x=2 \\ \\ x= \frac{2}{3}$