Questions: Solve the exponential equation. 3^x=20

Transcript text: Solve the exponential equation. \[ 3^{x}=20 \]

Solution

Step 1: Convert to Logarithmic Form

To solve the exponential equation \( 3^x = 20 \), we first convert it into logarithmic form. This gives us:

\[ x = \log_3(20) \]

Using the change of base formula, we can express this as:

\[ x = \frac{\log(20)}{\log(3)} \]

Step 2: Calculate the Logarithms

Next, we calculate the values of \( \log(20) \) and \( \log(3) \):

\[ \log(20) \approx 1.3010 \quad \text{and} \quad \log(3) \approx 0.4771 \]

Step 3: Compute the Value of \( x \)

Now, we substitute these values into our equation for \( x \):

\[ x \approx \frac{1.3010}{0.4771} \approx 2.7268 \]

Thus, the solution to the equation \( 3^x = 20 \) is

\[ \boxed{x \approx 2.7268} \]

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