Question

solve the equation for x
ln((2x+1)(x+2)) = 2 ln (x+2)
???? please help me!

Answer 1

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

Answer 2

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?

Answer 3

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.