Question

Sabendo que log5x= a log3x=b, determine log x raiz de 45 ao cubo

Answer 1

$log_{x}(5) = a \\ log_{x}(3) = b\\ log_{x}( \sqrt[3]{45} ) = ?$
Fatore o 45:

$log_{x}( \sqrt[3]{5 \cdot {3}^{2} } ) \\ = log_{x}{(5 \cdot {3}^{2} )}^{ \frac{1}{3} } \\ = \frac{1}{3} \cdot log_{x}{(5 \cdot {3}^{2} )} \\ = \frac{1}{3} (log_{x}(5) + log_{x}({3}^{2})) \\ = \frac{1}{3} (log_{x}(5) + 2 \cdot log_{x}(3)) \\ = \frac{1}{3} \cdot (a + 2b) \\ = \frac{1}{3}a + \frac{2}{3}b$
Espero ter ajudado! Bons estudos!