Question

Решите Уравнение: 0.4^5x+4 = 0.5 корней из 10

Answer 1

$0,4^{5x+4}=0,5 \sqrt{10}\\\\ ( \frac{2}{5})^{5x+4}= \frac{ \sqrt{2} \sqrt{5} }{2} \\\\ ( \frac{2}{5})^{5x+4}= \frac{2^{\frac{1}{2}}*5^{ \frac{1}{2} } }{2}\\\\ ( \frac{2}{5})^{5x+4}= \frac{5^{ \frac{1}{2} }}{2^{ \frac{1}{2} }}\\\\ ( \frac{2}{5})^{5x+4}= ( \frac{5}{2})^{ \frac{1}{2} }\\\\ ( \frac{2}{5})^{5x+4}= ( \frac{2}{5})^{-0,5}\\\\5x+4=-0,5\\\\5x=-4-0,5\\\\5x=-4,5\\\\x=-4,5:5\\\\x=-0,9$