matematica exercicios

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LEGENDA ^= elevado (potencia) * = vezes : = divisao / = fração
1) a) log3 27 => 3^x=27 => 3^x=3^3 =>X=3 
b) log1/5 125 => 1/5^x=125 => (5^-1)^x= 5^3 => 5^-x=5^3 => -x=3.(-1) =>x=-3
c) log4 raiz quadrada de 32
4^x=32^1/2 => (2^2)^x= 2^5*1/2 => (2^2)^x=2^5/2 => 2x=5/2 => x=5/2 : 2 => x=5/2*1/2 => x=5/4
d) log2/3 de 8/27 => 2/3^x= 8/27 => 2/3^x=(2/3)^3 => x=3
2)a) logx 8=3 => x^3=8 => x=2
b) logx 1/16=2 => x^2=1/16 => x=-+ Raiz de 1/16 => x=+-1/4
c) log2 x=5 => 2^5=X => x=32
d) log9 27=x => 9^x=27 => (3^2)^x=3^3 => 2x=3 => x=3/2
e) log1/2 32=x => 1/2^x=32 => 2^-x=2^5 => -x=5.(-1) => x=-5
3)a) log2 2^-3 => 2^x=2^-3 => x=-3
b) log7 raiz de 7 => 7^x=7^1/2 => x=1/2
c) 5^log5 7 => 5^log7 =>log5 7=x => 5^x=7 => 5^log5 7=5^x => 5^x=7 => 5^log5 7=7
4) log5 625 + log10 100 - log3 27 
log5 625 = x => 5^x=625 =>5^x = 5^4 ===> logo x=4 
log10 100 =y =>10^y=100 =>10^y=10² ===> logo y=2 
log3 27 = z => 3^z = 27 =>3^z = 3³ ===> logo =3 
Então log5 625 + log10 100 - log3 27 => 4+2-3 =3