Problem #WSP-000449

Problem

Using the fact that $\log_{10} (3) \approx 0.4771$ , $\log_{10} (5) \approx 0.698$ and $\log_{10} (6) \approx 0.778$ all correct to three or four decimal places (check), show that $5 \times 10^{47} < 3^{100} < 6 \times 10^{47}$ . How many digits does $3^{100}$ have, and what’s its first digit?

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