11- Resolva as equações exponenciais: a) 25^x =raiz de 5 R: 1/4
b) 49^²x+3=343 R: -3/4
e) (raiz de 5)2^x-2 = 1 R: 1
j) 32^x = 1/16 R:-4/5

1
e) (√5) 2 ×+²=1
ainda não entendi a (e) :)
( (raiz de 5) vezes 2 elevado a (x+2) ) = 1
isso
entendi..rrssrs... ;)

Respostas

2014-01-07T15:52:04-02:00
.a)

25^x= \sqrt{5} \\\\ (5^2)^x=5^( \frac{1}{2} ) \\\\ 2x= \frac{1}{2}  \\\\ \boxed{x= \frac{1}{4} }

b)

49^{2x+3}=343\\\\(7^2)^{2x+3}=7^3\\\\2(2x+3)=3\\\\4x+6=3\\\\4x=3-6\\\\\boxed{x=- \frac{3}{4}}

e)

( \sqrt{5} )^{2x-2}=1\\\\( \sqrt{5} )^{2x-2}=( \sqrt{5} )^0\\\\2x-2=0\\\\x= \frac{2}{2}\\\\\boxed{x=1}

j)

32^x= \frac{1}{16} \\\\32^x=16^{-1}\\\\(2^5)^x=(2^4)^{-1}\\\\2^{5x}=2^{-4}\\\\5x=-4\\\\\boxed{x=- \frac{4}{5} }

Espero ter ajudado.. :))