Solve `log(x+1)=2logx`

Solve log(-x)=2log(x+1)

Solve log_(4)(x-1)= log_(2) (x-3) .

Solve (log_(3)x)(log_(5)9)- log_x 25 + log_(3) 2 = log_(3) 54 .

Solve 4^(log_(2)logx)=logx-(logx)^(2)+1 (base is e).

Solve 4^logx =32 -x^log4 .

Solve log_(2)(3x-2)=log_((1)/(2))x

Solve for x:log(x+1)+log(x-1)=log99

Solve for x: a) (log_(10)(x-3))/(log_(10)(x^(2)-21)) = 1/2 b) log(log x)+log(logx^(3)-2)= 0, where base of log is 10. c) log_(x)2. log_(2x)2 = log_(4x)2 d) 5^(logx)+5x^(log5)=3(a gt 0), where base of log is 3. e) If 9^(1+logx)-3^(1+logx)-210=0 , where base of log is 3.