Answer:
Explanation:
We can start solving this equation by taking the logarithm of both sides of the equation, using any base we prefer. Let's use the natural logarithm, denoted by "ln":
ln(9^x) = ln((1/3)^(x+3))
Using the rule that ln(a^b) = b*ln(a) for any positive real number a and any real number b, we can simplify the left-hand side:
x*ln(9) = (x+3)*ln(1/3)
Next, we can simplify the right-hand side using the rule that ln(1/a) = -ln(a) for any positive real number a:
x*ln(9) = -(x+3)*ln(3)
Now we can solve for x by isolating it on one side of the equation. First, let's simplify the logarithmic terms using the fact that ln(9) = 2*ln(3):
2x*ln(3) = -(x+3)*ln(3)
Dividing both sides of the equation by ln(3), we get:
2x = -(x+3)
Simplifying and solving for x, we obtain:
2x = -x - 3
3x = -3
x = -1
Therefore, the solution to the equation 9^x = (1/3)^(x+3) is x = -1.