1. Given that

   $$2^{10}=1024\approx 1000$$

   show that

   $$10\ln (2)\approx 3\ln (10)$$

2. Given that

   $$e^3\approx 20$$

   show that

   $$\ln (2)+\ln (10)\approx 3$$

3. Hence, show that

   $$\ln (2)\approx \frac{9}{13}$$

   and

   $$\ln (10)\approx \frac{30}{13}$$

For (c), use "simultaneous equations" on the results from (a) and (b).