log_11(2x-1)=1-log_11(x+4) What is x?

1 Answer
Dec 17, 2017

log_11(2x-1)=1-log_11(x+4)

=>log_11(2x-1)+log_11(x+4)=1

=>log_11[(2x-1)(x+4)]=log_11 11
=>(2x-1)(x+4)]= 11

=>2x^2-x+8x-4- 11=0

=>2x^2+7x-15=0

=>2x^2+10x-3x-15=0

=>2x(x+5)-3(x+5)=0

=>(x+5)(2x-3)=0

So x=-5 and x=3/2

But x=-5 is not valid for the given equation log_11(2x-1)=1-log_11(x+4)

Hence x=3/2