QuestionSolve for $x$ : $$\begin{array}{l} \log (x+2)-\log (x+1)=1 \\ x=\square \end{array}$$
You may enter the exact value or round to 4 decimal places. Question Help: Video

Studdy Solution
Solve for $x$ by clearing the fraction. Multiply both sides by $x+1$:
$10(x+1) = x+2$
$10x + 10 = x + 2$
Subtract $x$ from both sides:
$10x - x + 10 = 2$
$9x + 10 = 2$
Subtract 10 from both sides:
$9x = 2 - 10$
$9x = -8$
Divide by 9:
$x = -\frac{8}{9}$
The value of $x$ is:
$$\boxed{-\frac{8}{9}}$$