Question

Решите уравнение.
$9 * (\frac{1}{4} )^x - 2 * (\frac{1}{2})^x = 0$

Answer 1

Ответ:

$9 \times {( \frac{1}{4}) }^{x} - 2 \times ( \frac{1}{2} ) {}^{x} = 0 \\ 9 \times ( \frac{1}{2} ) {}^{2x} - 2 \times ( \frac{1}{2} ) {}^{x} = 0 \\( \frac{1}{2} ) {}^{x} \times (9 \times ( \frac{1}{2} ) {}^{x} - 2) = 0 \\ \\ {( \frac{1}{2}) }^{x} = 0$

нет корней

$9 \times ( \frac{1}{2} ) {}^{x} - 2 = 0 \\ {( \frac{1}{2} )}^{x} = \frac{2}{9} \\ x = log_{ \frac{1}{2} }( \frac{2}{9} ) = log_{ \frac{1}{2} }(2) - log_{ \frac{1}{2} }(9) = \\ = - 1 - log_{ \frac{1}{2} }(9) = - 1 - log_{ {2}^{ - 1} }(9) = \\ = - 1 + log_{2}(9) = log_{2}(9) - 1$