Question

1-Determine o conjunto solução das equaçoes exponenciais:
a) 2^2x=256
b) 5^2x+1 = 1/625
c) 25^(x+2)=1
d) 64^x=16
e) 5^x²-16=1

Answer 1

a) 2^2x=256 ==> 2^2x = 2^8 ==> 2x=8 ==> x = 4
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b) 5^2x+1 = 1/625 ==> 5^2x+1 = 5^-4 ==>2x+1= - 4

==> 2x = - 4 -1 ==> 2x = - 5 ==> x = -5/2
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c) 25^(x+2)=1 ==> 25^(x+2) = 25^0 ==> x + 2 = 0 ==> x = - 2 
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d) 64^x=16 ==> (2^6)^x = 2^4 ==> 6x = 4 ==> x = 4/6
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e) 5^x²-16=1 ==> 5^x²-16= 5^0 ==> x²-16=0 ==> x²= +/-16 ==> x= +/- 4