Use properties of logartithms to simplify and solve. Thanks.
ln(x-3)-ln(11x-23)+in(x-1)=0
I believe it may be x=2,x=13
Did you test your answers?
Obviously x= 2 cannot be right since it would make
the second term undefined,
ln(22-23) = ln(-1), which is undefined
using the rules of logs, we get
ln[(x-3)(x-1)/(11x - 23) ] = 0
(x-3)(x-1)/(11x - 23) = e^0 = 1
x^2 - 4x + 3 = 11x - 23
x^2 - 15x+ 26 = 0
(x-2)(x-13) = 0
so x=2 or x=13
check for x=13
LS = ln10 - ln120 + ln12
= ln(10(12)/120) = ln 1 = 0 = RS
x = 13
To simplify and solve the equation ln(x-3) - ln(11x-23) + ln(x-1) = 0, we can use properties of logarithms.
First, combine the logarithms using the quotient property:
ln[(x-3)/(11x-23)] + ln(x-1) = 0
Next, we can use the sum property of logarithms to combine the two logarithms into one:
ln[(x-3)/(11x-23)(x-1)] = 0
To solve for x, we can take the exponential of both sides. Exponentiating both sides with base e (since ln represents the natural logarithm with base e), we get:
e^(ln[(x-3)/(11x-23)(x-1)]) = e^0
Now, the exponential of ln cancels out, leaving us with:
[(x-3)/(11x-23)(x-1)] = 1
To simplify the equation further, we can multiply both sides by (11x-23)(x-1):
(x-3) = (11x-23)(x-1)
Expand and simplify the right side of the equation:
x - 3 = 11x^2 - 12x - 23x + 23
Combining like terms:
x - 3 = 11x^2 - 35x + 23
Rearrange the equation to bring all terms to one side:
11x^2 - 36x + 26 = 0
Now, you can use the quadratic formula or any other appropriate method to solve for x.