calculus

Using the properties of logarithms, we can apply the property that allows us to combine like terms to rewrite the equation. First, note that on the left side of the equation, we are adding two logarithmic terms. According to the properties of logarithms, we can add the two logarithms to get the equation 3x-9=2*log3 + log(x+3)+(-log27). Now, if we look on the right side of the equation, we can combine the two negative terms. Since adding like terms allows us to combine, we can add -log27 and -log(x+3) together to get -log(27*(x+3)). Once we have done this, we can rearrange the equation to isolate the variable x which is done by subtracting 2*log3 from both sides and then divide both sides by 3. Thus, the equation can now be written as; x= (2*log3 + log(27*(x+3)))-9/(3) We can then solve for x by isolating the variable on one side of the equation. Thus, we can begin by multiplying both sides by 3, which gives us 3x = (2*log3+ log(27*(x+3)))-9.