• amyna
solve the equation for x ln((2x+1)(x+2)) = 2 ln (x+2) ???? please help me!
  • Stacey Warren - Expert
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  • jamiebookeater
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  • 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
  • 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?
  • 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.

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