Question

2. Expresa mediante un único logaritmo:
a) 2log x + 3logy - log5

b) 2+ log x - un medio de log y - log z​

Answer 1

A)

$2 log(x) + 3 log(y) - log(5) \\ = log( {x}^{2} ) + log({y}^{3} ) - log(5) \\ = log( {x}^{2} + {y}^{3} ) - log(5) \\ = log( \frac{ {x}^{2} + {y}^{3} }{5})$

B)

$2 + log(x) - \frac{ log(y) }{2} - log(z) \\ = 2 + log(x) - log( \sqrt{y} ) - log(z) \\ = log(100) + log(x) - log( \sqrt{y} ) - log(z) \\ = log(100 + x) - log( \sqrt{y} + z) \\ = log( \frac{100 + x}{ \sqrt{y} + z} )$