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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi!! Solve the logarithmic equation for x. ln(x - 4) + ln(x + 5) = 1 thanks for your help!      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28x-4%29%2Bln%28x%2B5%29=1 Start with the given equation.


ln%28%28x-4%29%28x%2B5%29%29=1 Combine the logs using the identity ln%28A%29%2Bln%28B%29=ln%28A%2AB%29


%28x-4%29%28x%2B5%29=e%5E1 Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> x=b%5Ey (note: the natural log has base "e")


%28x-4%29%28x%2B5%29=e Raise "e" to the first power to get "e"


%28x-4%29%28x%2B5%29=2.718 Replace "e" with its approximate decimal value


x%5E2%2Bx-20=2.718 FOIL


x%5E2%2Bx-20-2.718=0 Subtract 2.718 from both sides.


x%5E2%2Bx-22.718=0 Combine like terms.


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

x=-5.293 or x=4.293


However, since you cannot take the log of a negative number, this excludes x=-5.293.


So the only approximate solution is x=4.293