Find the value of x in sqrt(1+log_x(27))*log_3(x)+1=0?

1 Answer
Jul 17, 2018

sqrt(1+log_x(27))*log_3(x)+1=0
=>sqrt(log_3x*log_3x+3log_x(3)log_3(x)log_3x)=-1

=>log_3x*log_3x+3log_x(3)log_3(x)log_3x=1

=>(log_3x)^2+3log_3x-1=0

=>y^2+3y-1=0

=>y=(-3pmsqrt(9+4))/2

=>log_3x=(-3pmsqrt(9+4))/2

So log_3x=0.3028

=>x=3^(0.3028)~~1.4

Again
log_3x=-3.3

=>x=3^(-3.3)~~0.0265