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

Solve for x .
2^x=6

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

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Solution Steps

Step 1: Take the Logarithm of Both Sides

To solve the equation 2x=62^x = 6, we take the logarithm of both sides: log(2x)=log(6) \log(2^x) = \log(6)

Step 2: Apply the Logarithmic Property

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

Step 3: Solve for xx

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

Step 4: Calculate and Round the Result

Calculating the value gives us x2.584962500721156x \approx 2.584962500721156. Rounding this to four decimal places, we find: x2.585 x \approx 2.585

Final Answer

The solution to the equation 2x=62^x = 6 is x=2.585\boxed{x = 2.585}.

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