Question

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

A) logc (a³×b²)

Answer 1

Resposta:

logC (A³. B²) = 13

Explicação passo a passo:

logₓ A=6, logₓ B=4 e logₓ C=2 => logC (A³. B²) = ?

logₓ A=6 => x⁶ = A

logₓ B=4 => x⁴ = B

logₓ C=2 => x² = C

logC (A³. B²) = z =>  

$\displaystyle C^z = A^3. B^2\\\\(x^2)^z = (x^6)^3.(x^4)^2\\\\x^{2.z} = x^{6.3}.x^{4.2}\\\\x^{2z} = x^{18}.x^{8}\\\\x^{2z} = x^{18+8}\\\\x^{2z} = x^{26}\\\\2z=26\\\\z=\frac{26}{2} \\\\z=13$

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