Question

логарифм на фото математика

Answer 1

${6}^{ frac{2 - lg18}{lg36} } cdot {14}^{ frac{1 + lg5}{lg196} } ={(10^{lg6})}^{ frac{2 - lg18}{lg36} } cdot {(10^{lg14})}^{ frac{1 + lg5}{lg196} } = \ = 10^{ frac{lg6(2 - lg18)}{lg36} } cdot {10}^{ frac{lg14(1 + lg5)}{lg196} } = {10}^{ frac{2 - lg18}{ frac{lg36}{lg6} } + frac{1 + lg5}{ frac{lg196}{lg14} } } = \ = {10}^{ frac{2 - lg18}{log_6 36} + frac{1 + lg5}{log_{14}196} } = {10}^{ frac{2 - lg18}{log_6 6^2} + frac{1 + lg5}{log_{14}14^2} } = {10}^{ frac{2 - lg18}{2} + frac{1+lg5}{2} } = \ = {10}^{ frac{2 - lg18 + 1 + lg5}{2} } = ({10}^{3 + lg( frac{5}{18}) })^{ frac{1}{2} } = {( {10}^{3} cdot {10}^{lg( frac{5}{18} )} )}^{ frac{1}{2} } =$
$= {(1000 cdot frac{5}{18} )}^{ frac{1}{2} } = {( frac{2500}{9}) }^{ frac{1}{2} } = {( frac{ {50}^{2} }{ {3}^{2} }) }^{ frac{1}{2} } = ( {( frac{50}{3} )}^{2})^{ frac{1}{2} } = \ = frac{50}{3} = 16 frac{2}{3}$