Logarithm - SS2 Mathematics Past Questions and Answers - page 1

\(\log\sqrt[3]{462.3} = \ \frac{\log{462.3}}{3} = \ \frac{2.6649}{3} = \ 0.8883\) 

\(antilog\ 2.8837 = (characteristic = 2 + 1 = 3\ digits\ after\ the\ d.p.\ )\ \&\ \)

\(88\ under\ 3\ add\ difference\ 7 = \ 765.0\)

\(\log{0.00843} = \ \left( characteristic = 2 + 1 = 3 = \overline{3}\ \right)\ \&\ 84\ under\ 3 = \ \overline{3}.9258\)

\(\log\frac{246.8 \times 3.496}{43.69}\)

\[antilog\ 1.2955 = (characteristic = 1 + 1 = 2\ digits\ after\ the\ d.p.\ )\ \&\ \]

\(29\ under\ 5\ add\ difference\ 5 = \ 19.74\) 

\(\log 91^{2} = 2\log 91\ \)

\((characteristic = 2 - 1 = 1)\ \&\ 91\ under\ 0 = \ 1.9590\)

\(2 \times 1.9590 = \ 3.918\ \)

\(antilog\ 3.918 = 8279\)

\(\log\sqrt[2]{128} = \frac{\log 128}{2} = \ \frac{2.1072}{2} = \ 1.0536\)

\(antilog\ 1.0536 = 11.32\) 

a. \(30^{2}\)

Solution: \(\log 30^{2} = 2\log 30 = 2 \times 1.4771 = \ 2.9542\)

\[antilog\ 2.9542 = 899.9\ \approx 900\]

b. \(\sqrt[3]{1125}\)

Solution: \(\log\sqrt[3]{1125} = \frac{\log 1125}{3} = \frac{3.0512}{3} = \ 1.0171\)

\[antilog\ 1.0171 = 10.40\]

\(4^{x + 1} = 8^{x}\)

\(2^{2x + 2} = 2^{3x}\)

\(2x + 2 = 3x\)

\(2 = 3x - 2x\)

\(2 = x\)

\(x = 2\)