Solution to 3^(-x) = 9 is x = -2.
The equation 3^(-x) = 9 requires us to find the value of x that makes the left-hand side equal to 9. In other words, we need to find the exponent to which we raise 3 to get 9.
Here's how we can solve the equation:
1. Take the logarithm of both sides:
Applying the logarithmic property log_a(b^n) = n to both sides, we get:
-x * log_3(3) = log_3(9)
2. Simplify:
-x = log_3(9)
3. Solve for x:
Since log_3(9) = 2, we have:
-x = 2
4. Multiply both sides by -1:
x = -2
Therefore, the solution to the equation 3^(-x) = 9 is x = -2. This means that raising 3 to the power of -2 gives us 9: 3^(-2) = 9.
Question:
What is the solution to the equation
?