Given that \(\log_{10} 2 = 0.3010\) and \(\log_{10} 3 = 0.4771\), calculate without using mathematical tables or calculator, the value of : (a) \(\log_{10} ...

Assessment: WAEC SSCE - General Mathematics - 2001 (Essay) Subject: General Mathematics

Question 1 Report

Given that \(\log_{10} 2 = 0.3010\) and \(\log_{10} 3 = 0.4771\), calculate without using mathematical tables or calculator, the value of :

(a) \(\log_{10} 54\) ;

(b) \(\log_{10} 0.24\).

Answer

Answer Details

Given \(\log_{10}2=0.3010,\ \log_{10}3=0.4771\).

(a) \(54=2\times 27=2\times 3^{3}\).

\(\log_{10}54=\log_{10}2+3\log_{10}3=0.3010+3(0.4771)=0.3010+1.4313=\mathbf{1.7323}\).

(b) \(0.24=\dfrac{24}{100}=\dfrac{2^{3}\times 3}{100}\).

\(\log_{10}24=3\log_{10}2+\log_{10}3=0.9030+0.4771=1.3801\).

\(\log_{10}0.24=\log_{10}24-\log_{10}100=1.3801-2=\mathbf{-0.6199}\) (i.e. \(\bar{1}.3801\)).

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