SOLUTION: Hi!! Solve the logarithmic equation for x. ln(x - 4) + ln(x + 5) = 1 thanks for your help!

Question 199060: Hi!!
Solve the logarithmic equation for x.
ln(x - 4) + ln(x + 5) = 1
thanks for your help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Combine the logs using the identity

Rewrite the equation using the property: ====> (note: the natural log has base "e")

Raise "e" to the first power to get "e"

Replace "e" with its approximate decimal value

FOIL

Subtract 2.718 from both sides.

Combine like terms.

Now use either a calculator or the quadratic formula to get the approximate possible solutions:

or

However, since you cannot take the log of a negative number, this excludes .

So the only approximate solution is

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