Question

9*√27^x=3^x*√20.............

Answer 1

$9 times { (sqrt{27} )}^{x} = {3}^{x} times sqrt{20} \ \ {3}^{2} times {3}^{ frac{3x}{2} } = {3}^{x} times sqrt{20} \ \ {3}^{ frac{3x + 4}{2} } = {3}^{x} times sqrt{20} \ \ {3}^{ frac{3x + 4 - 2x}{2} } = sqrt{20} \ \ {3}^{ frac{x + 4}{2} } = sqrt{20} \ \ frac{x + 4}{2} = log_{3}( sqrt{20} ) \ \ x + 4 = 2 log_{3}( sqrt{20} ) \ \ x = 2 log_{3}( sqrt{20} ) - 4 = log_{3}(20) - log_{3}(81) = \ \ = log_{3}( frac{20}{81} )$

ОТВЕТ: log(3)_20/81