Question

log2 la 5=a log2 la 3=b atunci log15 la 12?

Answer 1

Folosesti formula: $log_{a}(b) = \frac{ log_{x}(b)}{ log_{x}(a)}$

$a= log_{15} (12) \\ b = log_{2}(3) \\ \\ log_{15}(12) = \frac{log_{2}(12)}{ log_{2}(15) } = \frac{log_{2}(4*3)}{ log_{2}(3*5) }=\\ = \frac{ log_{2}(4)+ log_{2}(3) }{ log_{2}(5) + log_{2}(3) } = \frac{2+b}{a+b}$