Решите уравнение(ПОМОГИТЕ ПЛЗ)ДАМ 20 БАЛ а)log5(x+1)-log5(4x+5)=0 б)log5(x)=2log5(3)+1/2log5(49)-1/3log5(27)
ОДЗ : 1) x + 1 > 0 ⇒ x > - 1 2) 4x + 5 > 0 ⇒ x > - 1,25 Окончательно x > - 1 Ответ: решений нет
![log _{5}x=2log _{5}3+ \frac{1}{2} log _{5} 49- \frac{1}{3} log _{5}27\\\\log _{5}x=log _{5} 9+log _{5} \sqrt{49}-log _{5} \sqrt[3]{27}\\\\log _{5}x=log _{5} 9+log _{5}7-log _{5}3\\\\log _{5}x=log _{5} \frac{9*7}{3}\\\\log _{5} x=log _{5}21\\\\x=21](https://tex.z-dn.net/?f=log+_%7B5%7Dx%3D2log+_%7B5%7D3%2B+%5Cfrac%7B1%7D%7B2%7D+log+_%7B5%7D+49-+%5Cfrac%7B1%7D%7B3%7D+log+_%7B5%7D27%5C%5C%5C%5Clog+_%7B5%7Dx%3Dlog+_%7B5%7D+9%2Blog+_%7B5%7D+%5Csqrt%7B49%7D-log+_%7B5%7D++%5Csqrt%5B3%5D%7B27%7D%5C%5C%5C%5Clog+_%7B5%7Dx%3Dlog+_%7B5%7D+9%2Blog+_%7B5%7D7-log+_%7B5%7D3%5C%5C%5C%5Clog+_%7B5%7Dx%3Dlog+_%7B5%7D+%5Cfrac%7B9%2A7%7D%7B3%7D%5C%5C%5C%5Clog+_%7B5%7D+x%3Dlog+_%7B5%7D21%5C%5C%5C%5Cx%3D21++++++++++++++ "log _{5}x=2log _{5}3+ \frac{1}{2} log _{5} 49- \frac{1}{3} log _{5}27\\\\log _{5}x=log _{5} 9+log _{5} \sqrt{49}-log _{5} \sqrt[3]{27}\\\\log _{5}x=log _{5} 9+log _{5}7-log _{5}3\\\\log _{5}x=log _{5} \frac{9*7}{3}\\\\log _{5} x=log _{5}21\\\\x=21")