The value of x satisfying 2log_9(2(1/2)^x-1)=log_27((1/4)^x-4)^3 is?

1 Answer
Aug 1, 2018

2log_9(2(1/2)^x-1)=log_27((1/4)^x-4)^3

=>2xxlog_9(27)log_27(2(1/2)^x-1)=log_27((1/4)^x-4)^3

=>2xxlog_9(9^(3/2))log_27(2(1/2)^x-1)=log_27((1/4)^x-4)^3
=>2xx3/2log_9(9)log_27(2(1/2)^x-1)=log_27((1/4)^x-4)^3

=>3log_27(2(1/2)^x-1)=log_27((1/4)^x-4)^3
=>log_27(2(1/2)^x-1)^3=log_27((1/4)^x-4)^3

=>(2(1/2)^x-1)=(((1/2)^x)^2-4)

Taking (1/2)^x=y we get

(2y-1)=(y^2-4)

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

=(y+1)(y-3)=0

So (1/2)^x=-1->"not possible"

And (1/2)^x=3

=>-xlog2=log3

=>x=-log3/log2