To solve the equation 2x=62^x = 62x=6, we take the logarithm of both sides: log(2x)=log(6) \log(2^x) = \log(6) log(2x)=log(6)
Using the property of logarithms, we can rewrite the left side: x⋅log(2)=log(6) x \cdot \log(2) = \log(6) x⋅log(2)=log(6)
Now, we isolate xxx by dividing both sides by log(2)\log(2)log(2): x=log(6)log(2) x = \frac{\log(6)}{\log(2)} x=log(2)log(6)
Calculating the value gives us x≈2.584962500721156x \approx 2.584962500721156x≈2.584962500721156. Rounding this to four decimal places, we find: x≈2.585 x \approx 2.585 x≈2.585
The solution to the equation 2x=62^x = 62x=6 is x=2.585\boxed{x = 2.585}x=2.585.
Oops, Image-based questions are not yet availableUse Solvely.ai for full features.
Failed. You've reached the daily limit for free usage.Please come back tomorrow or visit Solvely.ai for additional homework help.