Questions: Solve the exponential equation. Express irrational solutions in exact form. 3^x = 6 What is the exact answer? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Simplify your answer. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.) B. There is no solution.

Solution Steps

To solve the exponential equation \(3^x = 6\), we can take the natural logarithm of both sides to linearize the equation. This allows us to solve for \(x\) using properties of logarithms.

To solve the equation \(3^x = 6\), we take the natural logarithm of both sides: \[ \ln(3^x) = \ln(6) \]

Using the property of logarithms \(\ln(a^b) = b \ln(a)\), we can rewrite the equation as: \[ x \ln(3) = \ln(6) \]

Isolate \(x\) by dividing both sides by \(\ln(3)\): \[ x = \frac{\ln(6)}{\ln(3)} \]

Using the natural logarithm values: \[ x \approx \frac{1.7918}{1.0986} \approx 1.6309 \]

Final Answer