Final answer:
To solve the equation 2log(x+3)=log36+log4, apply the properties of logarithms. Combine the logarithms on the right side, simplify the left side, and solve for x.
Step-by-step explanation:
To solve the equation 2log(x+3)=log36+log4 using the properties of logarithms, we need to apply the logarithmic property that states log(ab) = log(a) + log(b). First, combine the two logarithms on the right side: log36+log4 = log(36*4) = log144. Now, the equation becomes 2log(x+3) = log144. Next, simplify the left side of the equation by using the property that states log(a^k) = k*log(a): log(x+3)^2 = log144. Taking the square root of both sides, we get x+3 = √144 = 12. Finally, subtract 3 from both sides to find the value of x: x = 12 - 3 = 9.