Question

Solve the equation 1 + 2log (x+1) = log (2x+1) = log (2x+1) +log (5x+8)

Answer 1

$1+2log(x+1)=log(2x+1)+log(5x+8).$

$log\frac{(2x+1)(5x+8)}{(x+1)^2}=1.$

$\frac{(2x+1)(5x+8)}{(x+1)^2}=10.$

$10x^2+16x+5x+8=10x^2+20x+10.$

$x=2.$