Use logarithms to evaluate: \( \sqrt[3]{\frac{(1.654)^{2}}{45.73 \times 0.56}}\)
| No. | Std. Form | Logarithm |
|---|---|---|
| \(1.654^2\) | \(1.654 \times 10^0\) | \(0.2185 \times 2 = 0.4370 \checkmark\) |
| \(45.73\) | \(4.573 \times 10^1\) | \(1.6602\) |
| \(0.56\) | \(5.6 \times 10^{-1}\) | \(\overline{1}.7482\) |
| \(1.4084 \checkmark\) | ||
| \(0.4745\) | \(4.7446 \times 10^{-1}\) | \(\overline{1}.6762\) |
\(\frac{\overline{1}.2 + 2.0286}{3} = \overline{1}.6762 \)
Kenya Certificate of Secondary Education, 2017
Use logarithms tables to evaluate: \[\sqrt[3]{\frac{6.72 \times (0.46)^2}{185.4}}\]
| No. | Std Form | Log |
|---|---|---|
| \(6.72\) | \(3.672 \times 10^1\) | \(1.5649\) |
| \(0.46\) | \(4.6 \times 10^{-1}\) | \(\overline{1}.6628 \times 2 = \overline{1}.3256\) |
| \(0.8905\) | ||
| \(185.4\) | \(1.854 \times 10^2\) | \(2.2681\) |
| \(2.6224\) | ||
| \(\frac{2.6224}{3}\) | ||
| \(=\overline{1}.5408\) | ||
| \(0.3474\) | \(3.474 \times 10^{-1}\) | \(\overline{1}.5408\) |
3. Evaluate \(\frac{76.12 \times 4087}{\sqrt{841.9}}\) correct to 3 S.F.
| No | Log |
|---|---|
| \(76.12\) | \(1.8815\) |
| \(\times 4087\) | \(+ 3.6115\) |
| Numerator | \(5.4930\) |
| \(5.4930\) | |
| \(841.9^{\frac{1}{2}}\) | \(2.9253 \div 2\) |
| Denominator | \(1.4627\) |
| \(-1.4627\) | |
| \(4.0303\) | |
| \(10730\) |
\(\frac{76.12 \times 4087}{\sqrt{841.9}} = 10730\)
| No. | Std Form | Log |
|---|---|---|
| \(83.46\) | \(8.346 \times 10^1\) | \(1.9215 + \) |
| \(0.0054\) | \(5.4 \times 10^{-3}\) | \(\overline{3}.7324 = \overline{1}.6539\) |
| \(1.56\) | \(1.56 \times 10^0\) | \(0.1931 \times 2\) |
| \(0.3862 \\ \overline{1}.6539 - 0.3862 = \overline{1}.2677 \) | ||
| \(0.5700\) | \(5.7 \times 10^{-1}\) | \(\overline{1}.7559\) |
\(\frac{\overline{3}}{3} + \frac{2.2677}{3} = \overline{1}.7559\)
use Logarithms to evaluate
\[\sqrt[3]{\frac{(1654)^{2}}{4573\times0.56}}\] (4 marks)
Solution
| No | Std | Log | |
|---|---|---|---|
| 1654 | \[(1.654\times10^{3})^{2}\] | 0.4316 | |
| 4573 | \[4.573\times10^{3}\] | 1.66026 | |
| 0.56 | \[5.6\times10^{-1}\] | \[\bar{1}.7482\] |
0.4744 \[= 4.744 \times 10^{-1}\]
\[\bar{1}.0286 \div 3\]
= 0.67625
|
N= (1.654)2 No Denominater 45.73 0.56 0.4744 |
(1.64×100)2 (1.64×102 4.573×101 5.6×10-1 4.1744×10-1 |
std 0.4370 1.6602 1.7482 1.4084 44.1744×10-1 |
log 0.4370 - 1.4084 -1.6762 T.02863 |
log 0.4370 - 1.4084 T.0286 ÷ 3 |