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Solve the following equation for x.​

Solve the following equation for x.​-example-1
User ArtemKha
by
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1 Answer

19 votes
19 votes

Answer:

If you just solve normally, you will get x=2 and x=-3. But if you plug these in to check your work, you will find that they are wrong. Your answer is no solution

Explanation:

ln(2x+3)+ln(x-2)=ln(x^2-2x)

Rule: log(a) + log(b) = log(a*b)

ln( (2x+3)(x-2) ) = ln(x^2-2x)

Rule: If log(a) = log(b) then a = b

(2x+3)(x-2) = x^2 - 2x

2x^2-x-6=x^2-2x

x^2+x-6=0

Using Quadratic Formula:

x = 2 and x = -3

But, plugging these numbers back into the original equation is false!

User ZedBee
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3.1k points