Alguém me ajuda .
S=log 0,001 base 100+log 4/9 base 3/2-log raiz cúbica 10 base 100
S=log 0,001 base 100+log 4/9 base 3/2-log raiz cúbica 10 base 100
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S=log 0,001 base 100+log 4/9 base 3/2-log raiz cúbica 10 base 100
S= log 0,001 + log 4/9 - log ∛10
100 3/2 100
Fazendo por partes que é melhor.
log 0,001 = x ==> 100^x = 0,001 ==> (10²)^x = 10^-3 => 2x = - 3 ==> x = -3/2
100
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log 4/9 = y ==> (3/2)^y = 4/9 ==> (3/2)^y = (2/3)² ==> (3/2)^y = (3/2)^-2
3/2
y = - 2
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log ∛10 = z
100
100^z = (10)^1/3 ==> (10²)^z = (10)^1/3 ==> 2z = 1/3 ==> 6z = 1 ==> 1/6
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- 3 + (-2) - 1 ==> - 3 - 2 - 1 ==> - 9 - 12 - 1 ==> - 22 ou - 11
2 6 2 6 6 6 3