Given the equation sin(x)=ln(x) determine an interval of length 1 that contains the root of the equation

1. Let's define the functions f(x) = \sin(x) - \ln(x) and evaluate it at some points to find a sign change:

- Evaluate at x = 1:
\sin(1) \approx 0.8415 and \ln(1) = 0, so f(1) \approx 0.8415.

- Evaluate at x = 2:
\sin(2) \approx 0.9093 and \ln(2) \approx 0.6931, so f(2) \approx 0.9093 - 0.6931 = 0.2162.

- Evaluate at x = 3:
\sin(3) \approx 0.1411 and \ln(3) \approx 1.0986, so f(3) \approx 0.1411 - 1.0986 = -0.9575.

2. Since f(2) > 0 and f(3) < 0, by the Intermediate Value Theorem, there is a root between x = 2 and x = 3. The interval of length 1 containing the root is:

Answer: [2, 3].