Using the fact that \(\log_{10}(3)\approx0.4771\), \(\log_{10}(5)\approx0.698\) and \(\log_{10}(6)\approx0.778\) all correct to three or four decimal places (check), show that \(5\times10^{47}<3^{100}<6\times10^{47}\). How many digits does \(3^{100}\) have, and what’s its first digit?