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Given log₁₀(2) = 0.3010 and log₁₀(3) = 0.4771, let P be the number of digits in 4⁸ * 3⁵ * 5³. Find the value of (P - 1) / 2.

1. 1
2. 2
3. 3
4. 4

Correct answer: 4

Solution

log₁₀(4⁸ * 3⁵ * 5³) = 8*log₁₀(4) + 5*log₁₀(3) + 3*log₁₀(5) = 8*(2*0.3010) + 5*0.4771 + 3*(0.6990) = 4.816 + 2.3855 + 2.097 = 9.2985. So P = 9 + 1 = 10... giving (P-1)/2 = 4.5, nearest integer option is 4.

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