Questions: Question 5, 5.3.23 Solve the logarithmic equation. log3 x=4 x= (Simplify your answer. Type an exact answer, using e as needed.)

Transcript text: Question 5, 5.3.23 Solve the logarithmic equation. \[ \begin{array}{l} \log _{3} x=4 \\ x=\square \end{array} \] $\square$ (Simplify your answer. Type an exact answer, using $e$ as needed.)

Solution

Solution Steps

To solve the logarithmic equation $\log_{3} x = 4$, we need to convert the logarithmic form to its equivalent exponential form. The equation $\log_{b} a = c$ can be rewritten as $b^c = a$. Applying this to our equation, we get $3^4 = x$.

Step 1: Convert Logarithmic to Exponential Form

We start with the logarithmic equation: \[ \log_{3} x = 4 \] To convert this to exponential form, we use the definition of logarithms: \[ x = 3^4 \]

Step 2: Calculate the Exponent

Now we calculate $3^4$: \[ 3^4 = 81 \]