lnX + ln2 = 3
Use the law of exponent:
lnA+lnB=ln(A*B)
So
lnX+ln2=3
ln(2X)=3
raise to power of e:
e^(ln(2X) = e^3
2X=e^3 [because e^lnY=Y ]
X=(e^3)/2
To solve the equation ln(X) + ln(2) = 3, we can use the properties of logarithms.
First, we can simplify the equation by combining the logarithms using the property that ln(a) + ln(b) = ln(ab). So we have ln(X * 2) = 3.
Next, we can apply the definition of logarithms, which states that logₐ(b) = c if and only if a^c = b. In this case, we have ln(X * 2) = 3, which means e^3 = X * 2, where e is the base of the natural logarithm.
Now, we can solve for X by dividing both sides of the equation by 2: X = e^3 / 2.
Therefore, the solution to the equation ln(X) + ln(2) = 3 is X = e^3 / 2.