Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
31-x = 1/27
Assuming you mean
3^(1-x) = 1/27
3^(1-x) = 3^(-3)
1-x = -3
x = 4
To solve the exponential equation 31-x = 1/27, we can rewrite both sides of the equation as powers of the same base. In this case, the base is 3 since 27 is equal to 3^3.
Step 1: Express 31 as a power of 3
31 = 3^x
Step 2: Rewrite 1/27 as a power of 3
1/27 = (3^-3)
Now, we can equate the exponents:
3^x = 3^-3
Since the bases are the same, the exponents must be equal:
x = -3
Therefore, the solution to the equation 31-x = 1/27 is x = -3.