Question

Sendo logx (2)= a, logx (3)=b calcule logx ³√12


Me ajudem por favor amigos.

Answer 1

Resposta:

(2a+b)/3

Explicação passo-a-passo:

Temos que:

logx ³√12 =

logx 12^(1/3) =

(1/3). logx 12 =

(1/3). logx 4.3 =

(1/3). logx (2^2). 3 =

(1/3). [logx 2^2 + logx 3] =

(1/3). [2.logx 2 + logx 3] =

Como logx 2= a, logx 3=b, temos:

(1/3). [2.a + b] =

(2a+b)/3

Blz?

Abs :)

Answer 2

$log_{x}( \sqrt[3]{12} ) = log_{x}( \sqrt[3]{ {2}^{2}.3} ) \\ = log_{x}( \sqrt[3]{ {2}^{2} } ) + log_{x}( \sqrt[3]{3} )$

$log_{x}( {2})^{ \frac{2}{3} } + log_{x}({3})^{ \frac{1}{3} } \\ \frac{2}{3} log_{x}(2) + \frac{1}{3} log_{x}(3) \\ = \frac{2}{3}a + \frac{1}{3}b$