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