Question

Решите неравенство
${5}^{x} - { 3}^{x - 1} > 2(5 {}^{x - 1} - {3}^{x - 2} )$
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Answer 1

Ответ:

${5}^{x} - {3}^{x - 1} > 2( {5}^{x - 1} - {3}^{x - 2} ) \\ {5}^{x} - {3}^{x - 1} > 2 \times {5}^{x - 1} - 2 \times {3}^{x - 2} \\ {5}^{x} - 2 \times {5}^{x - 1} > {3}^{x - 1} - 2 \times {3}^{x - 2} \\ {5}^{x - 1} (5 - 2) > {3}^{x - 1} (1 - 2 \times {3}^{ - 1} ) \\ {5}^{x - 1} \times 3 > {3}^{x - 1} \times \frac{1}{3} \\ \frac{ {5}^{x - 1} }{ {3}^{x - 1} } > \frac{1}{9} \\ {( \frac{5}{3}) }^{x - 3} > \frac{1}{9} \\ x - 1 > log_{ \frac{5}{3} }( \frac{1}{9} ) \\ x - 1 > log_{ \frac{5}{3} }( {3}^{ - 2} ) \\ x - 1 > - 2 log_{ \frac{5}{3} }(3) \\ x > 1 - 2 log_{ \frac{5}{3} }(3)$