Question

3∙7^(х+2) - 14*7^х=686 Помогите решить! Пожалуйста!

Answer 1

$3 \times {7}^{x + 2} - 14 \times {7}^{x} = 686 \\ 3 \times {7}^{x} \times {7}^{2} - 14 \times {7}^{x} = 686 \\ замена \\ {7}^{x} = y \\ 3 \times 49 \times y -14 \times y = 686 \\ 147y - 14y = 686 \\ 133y = 686 \\ y = \frac{686}{133} = \frac{686 \div 7}{133 \div 7} = \frac{98}{19} \\ замена обратно \\ {7}^{x} = \frac{98}{19} \\ x = log_{7}( \frac{98}{19} ) \\ x = log_{7}( \frac{49 \times 2}{19} ) = log_{7}(49 \times \frac{2}{19} ) \\ x = log_{7}(49) + log_{7}( \frac{2}{19} ) \\ x = 2 + log_{7}( \frac{2}{19} )$