Questions: Solve for x . 2^x=6 Solve for x . A. x=

Transcript text: Solve for x . \[ 2^{x}=6 \] Solve for x . A. $\mathrm{x}=$ $\square$

Solution

Step 1: Take the Logarithm of Both Sides

To solve the equation $2^x = 6$, we take the logarithm of both sides: \[ \log(2^x) = \log(6) \]

Step 2: Apply the Logarithmic Property

Using the property of logarithms, we can rewrite the left side: \[ x \cdot \log(2) = \log(6) \]

Step 3: Solve for $x$

Now, we isolate $x$ by dividing both sides by $\log(2)$: \[ x = \frac{\log(6)}{\log(2)} \]

Step 4: Calculate and Round the Result

Calculating the value gives us $x \approx 2.584962500721156$. Rounding this to four decimal places, we find: \[ x \approx 2.585 \]

The solution to the equation $2^x = 6$ is $\boxed{x = 2.585}$.

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