Solve the following exponential function for x if f(x) is equal to 9:

f(x) = 81x

Question

Solve the following exponential function for x if f(x) is equal to 9:

f(x) = 81x

BlackTom AI · Accepted Answer

The problem statement appears to have a notation issue: f(x) = 81x likely intends f(x) = 81^x, since the given answer is x = 1/2 and that corresponds to solving 81^x = 9.

Step 1: Recognize the equation to solve is 81^x = 9, not 81x = 9. If the expression were 81x, the solution would be x = 9/81 = 1/9, which does not match the provided answer. The consistency with the given answer suggests an exponential form rather than a linear form.

Step 2: Express both sides with the same base. Note that 81 = 3^4 and 9 = 3^2. Using these, rewrite the equation as (3^4)^x = 3^2.

Step 3: Apply the power rule for exponents: (3^4)^x = 3^{4x}. So 3^{4x} = 3^2.

Step 4: Since the bases are identical and positive, set the exponents equal: 4x = 2.

Step 5: Solve for x: x = 2/4 = 1/2.

If the original statement truly meant f(x) = 81x (a linear function), the equation 81x = 9 would yield x = 1/9, which is a different result. The discrepancy highlights the importance of the correct functional form (exponential vs. linear) for solving the problem. In the absence of explicit answer options, this reasoning shows how to arrive at x = 1/2 when interpreting f(x) as 81^x.

CO.BU.Quantitative_Business_Prep Module 1 Quiz

Solve the following exponential function for x if f(x) is equal to 9: f(x) = 81x

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