question\nsolve for $x$ to the nearest 10th.\n$11 = 800(0.5)^{\frac{x}{13}}$

Answer:

$x \approx 60.6$

Explanation:

Step1: Isolate the exponential term

Divide both sides by 800: $\frac{11}{800} = (0.5)^{\frac{x}{13}}$

Step2: Take natural log of both sides

Use log property $\ln(a^b)=b\ln(a)$: $\ln\left(\frac{11}{800}\right) = \frac{x}{13}\ln(0.5)$

Step3: Solve for x

Rearrange to isolate x: $x = 13 \times \frac{\ln\left(\frac{11}{800}\right)}{\ln(0.5)}$

Step4: Calculate the value

Compute the logs and simplify: $\ln\left(\frac{11}{800}\right) \approx \ln(0.01375) \approx -4.281$ $\ln(0.5) \approx -0.6931$ $x \approx 13 \times \frac{-4.281}{-0.6931} \approx 13 \times 6.177 \approx 60.6$