Question 461053: I tried to solve this in all my calculators I have and all of them say unable to solve this type of logarithm even tho all of them have the (ln) function. Here is the equation
2ln(x-3)=ln(x+5)+ln4
When I input it in it asks if i'm solving for x or e.. not sure where the are getting the e from but anyway.. any help would be appreciated.
Found 2 solutions by ankor@dixie-net.com, richard1234:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 2*ln(x-3) = ln(x+5) + ln(4)
You don't need a calc to solve this
:
We can re-write this using the rules of exponents and logs
ln((x-3)^2) = ln(4(x+5))
therefore
(x-3)^2 = 4(x+5)
FOIL
x^2 - 6x + 9 = 4x + 20
x^2 - 6x - 4x + 9 - 20 =
x^2 - 10x - 11 = 0
Factor this
(x-11)(x+1) = 0
Two solutions
x = 11, the only good solution
and
x = -1, you can't have a log of a neg, so this won't work
:
:
But you can use a calc to check it: enter:
2*ln(11-3) = 4.15888
enter
ln(11+5) + ln(4) = 4.15888; equality reigns, so x=11 is a good solution
Answer by richard1234(7193)  (Show Source):
You can put this solution on YOUR website! Some calculators do not have the ln function, in which you can input it as the log base e (this is rare though, most calculators that allow log of any base will automatically have an ln button). Be careful that if you input e, it must be the constant e, not the variable e.
However you do not need a calculator to solve it. Follow the other tutor's solution, using the properties of logarithms, and it becomes a simple quadratic equation.
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