Answer to Question #247921 in Algebra for jon jones

Question

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

Answer 1

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

$$\begin{matrix} x+1>0 \\ 2x+1>0 \\ 5x+8>0 \end{matrix}=>x>-\dfrac{1}{2}$$

Then

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

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

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

$$x=2$$

$$2>-\dfrac{1}{2}$$

Answer: $x=2.$