Questions: Solve for (x) in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. [2^x+2=6] [x=]

Solution Steps

We start with the equation: \[ 2^{x+2} = 6 \] Taking the natural logarithm of both sides gives us: \[ \ln(2^{x+2}) = \ln(6) \]

Using the property of logarithms that states \( \ln(a^b) = b \cdot \ln(a) \), we can rewrite the left side: \[ (x+2) \cdot \ln(2) = \ln(6) \]

Next, we isolate \( x \): \[ x + 2 = \frac{\ln(6)}{\ln(2)} \] \[ x = \frac{\ln(6)}{\ln(2)} - 2 \]

After performing the calculations, we find: \[ x \approx 0.5849625007211561 \] Rounding this to the nearest hundredth gives: \[ x \approx 0.58 \]

Final Answer