Question

Решите пример с логарифмами

Answer 1

$\displaystyle \large \boldsymbol{} \frac{log_512-log_5 4}{log_518+log_50,5} -\frac{lg 64+lg0,5}{lg7-lg14}=\\\\ \\\frac{log_5(12:4)}{log_5(18*0,5)} -\frac{lg(64*0,5)}{lg(7:14)}=\frac{log_53}{log_59} -\frac{lg32}{lg0,5}= \\\\ \\\frac{log_53}{log_53^2} -\frac{lg2^5}{lg2^-^1}=\frac{log_53}{2log_53} -\frac{5lg2}{-1lg2}= \frac{1}{2}-\frac{5}{-1} =\frac{1}{2} +5=\\\\\\\frac{1}{2} +\frac{10}{2} =\frac{11}{2} =\boldsymbol{5\frac{1}{2} }$