Logarithm - SS2 Mathematics Past Questions and Answers - page 1
Find the logarithm of \(\sqrt[3]{462.3}\)
2.6649
0.3010
1.4645
0.8883
\(\log\sqrt[3]{462.3} = \ \frac{\log{462.3}}{3} = \ \frac{2.6649}{3} = \ 0.8883\)
Evaluate \(antilog\ 2.8837\)
345
724
765
476
\(antilog\ 2.8837 = (characteristic = 2 + 1 = 3\ digits\ after\ the\ d.p.\ )\ \&\ \)
\(88\ under\ 3\ add\ difference\ 7 = \ 765.0\)
Calculate \(\log{0.00843}\)
2.4567
\(\overline{2}.9069\)
\(\overline{3}.9258\)
1.0987
\(\log{0.00843} = \ \left( characteristic = 2 + 1 = 3 = \overline{3}\ \right)\ \&\ 84\ under\ 3 = \ \overline{3}.9258\)
Find the logarithm of \(\frac{246.8 \times 3.496}{43.69}\)
19.74
18.89
13.74
15.77
\(\log\frac{246.8 \times 3.496}{43.69}\)
| NUMBER | LOGARITHM | |
|---|---|---|
| \[246.8\] | \[2.3923\] | |
| \[3.496\] | \[0.5436\] | |
| \[2.3923 + 0.5436 = 2.9359\] | ||
| \[43.69\] | \[1.6404\] | |
| \[2.9359 - 1.6404 = 1.2955\] |
\[antilog\ 1.2955 = (characteristic = 1 + 1 = 2\ digits\ after\ the\ d.p.\ )\ \&\ \]
\(29\ under\ 5\ add\ difference\ 5 = \ 19.74\)
Using the logarithm table, find the square of \(91\)
8767
8279
7678
8267
\(\log 91^{2} = 2\log 91\ \)
\((characteristic = 2 - 1 = 1)\ \&\ 91\ under\ 0 = \ 1.9590\)
\(2 \times 1.9590 = \ 3.918\ \)
\(antilog\ 3.918 = 8279\)
Calculate the square of \(128\) using the log table.
11.32
12.23
10.89
11.58
\(\log\sqrt[2]{128} = \frac{\log 128}{2} = \ \frac{2.1072}{2} = \ 1.0536\)
\(antilog\ 1.0536 = 11.32\)
Evaluate the following using the log table:
-
-
\(30^{2}\)
-
\(\sqrt[3]{1125}\)
-
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: \(\log\sqrt[3]{1125} = \frac{\log 1125}{3} = \frac{3.0512}{3} = \ 1.0171\)
\[antilog\ 1.0171 = 10.40\]
Solve for \(x\) in the equation \(4^{x + 1} = 8^{x}\)
\(4^{x + 1} = 8^{x}\)
\(2^{2x + 2} = 2^{3x}\)
\(2x + 2 = 3x\)
\(2 = 3x - 2x\)
\(2 = x\)
\(x = 2\)