WAEC Mathematics 2020 Paper

Concept:To combine a number with a logarithm, convert the number into a logarithm using the same base, then apply the power and product rules.Explanation:The given expression is $1 + 2\log_{10} 3$.Any number $a$ can be written as $\log_{10} 10^a$. Therefore, $1 = \log_{10} 10$.The power rule states $n\log_b x = \log_b x^n$. Thus, $2\log_{10} 3 = \log_{10} 3^2 = \log_{10} 9$.Now the expression becomes $\log_{10} 10 + \log_{10} 9$.Using the product rule, $\log_{10} 10 + \log_{10} 9 = \log_{10} (10 \times 9)$.Since $10 \times 9 = 90$, the expression simplifies to $\log_{10} 90$.Answer:$\log_{10} 90$, which is option A.