Question

Calcule o valor dos seguintes logaritmos:a) Log 16 64 f) log 49 ∛7 g)log ( 9 ( 3√3)b) log 5 ( 0,000064)c) log( 5√2) 128 h)log 2 0,25d) log2 ( 8√64)e) log625√5

Answer 1

a) Log 16 64 = x ==> 16^x = 64 ==> 4^x = 4^3 ==> x = 3

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f) log 49 ∛7 = y ==> 49^y =∛7 ==> (7^2)^y = 7^1/3 ==> 2y = 1/3==>y = 1/6

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g)log ( 9 ( 3√3) = 9^w = 3V3 ==> (3^2)^w = 3.3^1/13 ==> 3^2w = 3^4/3

==>2w  = 4/3 ==> w = 4/6

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b) log 5 ( 0,000064) = 5^t = 2^6 .10^-6  bases diferentes

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c) log( 5√2) 128 = e ==> (5.2^1/2)^e = 2^7  bases  diferentes

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h)log 2 0,25 = t ==> 2^t = (2^-1)^4 ==> 2^t = 2^-4 ==> t = - 4

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d) log2 ( 8√64) = s ==> 2^s = 2^3.(2^6)^1/2 ==> 2^s = 2^3.2^6/2

2^s = 2^3.2^3 ==> 2^s = 2^(3+3) ==> s = 3+3 ==> s = 6

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e) log625√5 = (5^1/2)^x = 5^4 ==> 5^x/2 = 5^4 ==> x /2 = 4 ==>x = 8