Question

Помогите решить пример по алгебре , 60 баллов
x−1+log4 3=log4 (5x−4x−1)

Answer 1

$x-1+log_4(3)=log_4(5^x-4^{x-1})\\log_4(5^x-4^{x-1})=x-1+ \frac{1}{2} log_2(3)\\5^x-4^{x-1}=4^{x-1+ \frac{1}{2} log_2(3)}\\5^x-2^{2x}* \frac{1}{4} =2^{2x}*2{-2}*2^{log_2(3)}\\5^x-4^x* \frac{1}{4} =4^x*2^{-2}*3\\5^x-\frac{4^x}{4} =3*\frac{4^x}{4} \\5^x=\frac{3*4^x}{4} +\frac{4^x}{4} \\5^x=\frac{3*4^x+4^x}{4} \\5^x=4^x\\(\frac{5}{4} )^x=(\frac{5}{4} )^0\\x=0\\5^x-4^{x-1}\ \textgreater \ 0\\5^x\ \textgreater \ 4^{x-1}\\x\ \textgreater \ 2log_5(2)x-2log_5(2)\\(1-2log_5(2))x\ \textgreater \ -2log_5(2)\\x\ \textgreater \ -2log_{\frac{5}{4} }(2)$