## amyna one year ago solve the equation for x ln((2x+1)(x+2)) = 2 ln (x+2) ???? please help me!

1. Vocaloid

well, let's look at the right side 2*ln(x+2) using our log rules, we can move the 2 and make it an exponent, giving us: ln(x+2)^2

2. Vocaloid

now, we're left with ln((2x+1)(x+2)) = ln (x+2)^2 we can "cancel" the log by raising both sides to the base of e, giving us (2x+1)(2x+2) = (x+2)^2 can you take it from here?

3. tkhunny

Be very, very careful about Domain issues. For $$2\cdot\ln(x+2)$$, we have $$x \gt -2$$. For $$\ln\left[(x+2)^{2}\right]$$, we have $$x \ne -2$$. We changed something! So, also the left hand side. Very careful, indeed.