Question

Sendo logx A=6, logx B=4 e logx C=2 , calcule :

A) logc (a³×b³

Answer 1

Resposta:

logC (A³. B³) = 15

Explicação passo a passo:

logₓ A=6, logₓ B=4 e logₓ C=2 => logC (A³. B³) = ?

logₓ A=6 => x⁶ = A

logₓ B=4 => x⁴ = B

logₓ C=2 => x² = C

logC (A³. B³) = z =>  

$\displaystyle C^z = A^3. B^3=(A.B)^3\\\\(x^2)^z = (x^6.x^4)^3\\\\x^{2z} = (x^{6+4})^3\\\\x^{2z} = (x^{10})^3\\\\x^{2z} = x^{10.3}\\\\x^{2z} = x^{30}\\\\2z=30\\\\z=\frac{30}{2} \\\\z=15$

$Propriedades:\\(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \\\\a^{0}=1\\\\a^{1}=a$