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