The value of x if, ln3+2lnx=ln(x+2) is
First, we can use the rule of logarithms that states ln(a) + ln(b) = ln(ab) to simplify the equation:
ln(3) + ln(x^2) = ln(x+2).
Next, we can use the rule of logarithms that states ln(a^b) = b * ln(a) to further simplify the equation:
ln(3x^2) = ln(x+2).
Now, we can remove the natural logarithm from both sides of the equation using the property that states if ln(a) = ln(b), then a = b:
3x^2 = x + 2.
Rearranging the equation, we get:
3x^2 - x - 2 = 0.
To solve this quadratic equation, we can factorize it:
(3x + 2)(x - 1) = 0.
Setting each factor to zero and solving for x, we get two possible solutions:
3x + 2 = 0, x = -2/3.
x - 1 = 0, x = 1.
So, the possible values of x are -2/3 and 1.