The value of x if, ln3+2lnx=ln(x+2) is

Answer 1

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.