Question

Determine o valor da expressao log5 28 considerando log 2=0,3 log 5=0,7 e log log 7=0,8.?

Answer 1

$\mathrm{\ell og}_{5}\,28=\frac{\mathrm{\ell og\,} 28}{\mathrm{\ell og\,} 5}\\ \\ =\frac{\mathrm{\ell og}\left(2^{2}\times 7 \right )}{\mathrm{\ell og\,} 5}\\ \\ =\frac{\mathrm{\ell og}\left(2^{2} \right )+\mathrm{\ell og\,}{7}}{\mathrm{\ell og\,} 5}\\ \\ =\frac{2\,\mathrm{\ell og\,}{2}+\mathrm{\ell og\,} 7}{\mathrm{\ell og\,} 5}\\ \\ =\frac{2 \times 0,3+0,8 }{0,7}\\ \\ =\frac{0,6+0,8}{0,7}\\ \\ =\frac{1,4}{0,7} \Rightarrow \boxed{\mathrm{\ell og}_5\,{28}=2,0}$