Resolvem isso que esta no print pfv
Resolvem isso que esta no print pfv
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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}]()
![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}](/image/0193/4436/0e66d.png)
![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}](/image/0193/4436/4540a.png)
2)
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