Solve the following exponential equation. Express irrational solutions in exact

Question

Solve the following exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3^x = 4 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. Type an exact answer.) B. There is no solution. What is the answer rounded to three decimal places? 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. Type an integer or decimal rounded to three decimal places as needed.) B. There is no solution.

Explanation / Answer

We have 3x =4. On taking logarithm of both the sides, we get log(3x) = log 4 or, x log 3 = log 4 . Therefore, x = log 4/log 3 = 0.602059991/ 0.477121254 = 1.261859508 = 1.262 (on rounding off to 3 decimal places).

The exact answer is x = (log 4)/(log3).

The answer, rounded to 3 decimal places is x = 1.262.

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