Solve the following exponential equation.
\[
3^{\mathrm{x}}=8
\]
Select the correct choice below and, if necessary, fill in the answer box.
A. $x=8$
(Round to three decimal places as needed. Use a comma to separat
B. The solution is not a real number.

Answer

Expert–verified

Hide Steps

Answer

$\boxed{x \approx 1.893}$ is the solution to the equation $3^x = 8$.

Steps

Step 1 ：Given the exponential equation $3^x = 8$.

Step 2 ：We can solve for x by taking the natural logarithm (ln) of both sides. This gives us $x \cdot ln(3) = ln(8)$.

Step 3 ：Solving for x, we get $x = \frac{ln(8)}{ln(3)}$.

Step 4 ：Calculating the above expression, we find that $x \approx 1.893$.

Step 5 ：$\boxed{x \approx 1.893}$ is the solution to the equation $3^x = 8$.