Question

sendo log2= 0.3 ; log3=0.4 e log5= 0,7 determine log2 na base 9

Answer 1

$\mathrm{\ell og}_{9\,}2=\dfrac{\mathrm{\ell og\,}2}{\mathrm{\ell og\,}9}\\ \\ \\ \mathrm{\ell og}_{9\,}2=\dfrac{\mathrm{\ell og\,}2}{\mathrm{\ell og\,}(3^{2})}\\ \\ \\ \mathrm{\ell og}_{9\,}2=\dfrac{\mathrm{\ell og\,}2}{2\,\mathrm{\ell og\,}3}\\ \\ \\ \mathrm{\ell og}_{9\,}2=\dfrac{0,3}{2\cdot 0,4}\\ \\ \\ \mathrm{\ell og}_{9\,}2=\dfrac{0,3}{0,8}\\ \\ \\ \mathrm{\ell og}_{9\,}2=\dfrac{3}{8}\\ \\ \\ \mathrm{\ell og}_{9\,}2=0,375$