Question 461053
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