Question

Si Log2 5= a. Calcula Log40 500.

Answer 1

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$\mathsf{si : } \: \: \: \: \log_{2} 5 = a$

Calcula:

$\log_{40} 500 = \frac{\log_{2}{500} }{ \log_{2}{40}} = \frac{\log_{2} (125\cdot 4) }{ \log_{2} (5\cdot 8) }$

$= \frac{\log_{2} 125+ \log_{2} 4 }{ \log_{2} 5+\log_{2} 8 } = \frac{3\log_{2} 5+ 2\log_{2} 2 }{ \log_{2} 5+3\log_{2} 2 }$

$\frac{3\log_{2} 5 \: + \: 2\log_{2} 2 }{ \log_{2} 5 \: + \: 3\log_{2} 2 } =\boxed{ \frac{ 3a + 2 }{a +3 } }$