Question

dado log4= 0,62, calcule o valor de log 32^5

Answer 1

$\mathrm{\ell og\,}4=0,62\\ \\ \mathrm{\ell og\,}(2^{2})=0,62\\ \\ 2\mathrm{\,\ell og\,}2=0,62\\ \\ \mathrm{\ell og\,}2=\dfrac{0,62}{2}\\ \\ \mathrm{\ell og\,}2=0,31\;\;\;\;\;\mathbf{(i)}$


$\mathrm{\ell og\,}(32^{5})\\ \\ =\mathrm{\ell og\,}[(2^{5})^{5}]\\ \\ =\mathrm{\ell og\,}[2^{5\,\cdot\,5}]\\ \\ =\mathrm{\ell og\,}[2^{25}]\\ \\ =25\mathrm{\,\ell og\,}2\\ \\ =25\cdot 0,31\\ \\ =7,75\\ \\ \\ \Rightarrow\;\;\boxed{\mathrm{\ell og\,}(32^{5})=7,75}$