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3. If \log 31.09=1.4926 find the value of the following without using \log table.(v) \log 310.942
3. If  \log 31.09=1.4926  find the value of the following without using  \log  table.(v)  \log 310.942

3. If \log 31.09=1.4926 find the value of the following without using \log table.(v) \log 310.942

1. Find the common logarithm of each of the following numbers.(ii) 29.326
1. Find the common logarithm of each of the following numbers.(ii)  29.326

1. Find the common logarithm of each of the following numbers.(ii) 29.326

5. Evaluate (i) \log _{2} \frac{1}{128}
5. Evaluate (i)  \log _{2} \frac{1}{128}

5. Evaluate (i) \log _{2} \frac{1}{128}

3. If \log 31.09=1.4926 find the value of the following without using \log table.(ii) \log 310.9
3. If  \log 31.09=1.4926  find the value of the following without using  \log  table.(ii)   \log 310.9

3. If \log 31.09=1.4926 find the value of the following without using \log table.(ii) \log 310.9

3. Find the value of x from the following using calculator.(viii) \log x=\overline{2} .7777
3. Find the value of  x  from the following using calculator.(viii)  \log x=\overline{2} .7777

3. Find the value of x from the following using calculator.(viii) \log x=\overline{2} .7777

1. Find the values of the following by using logarithms.(ii) 25.753 \times 0.5341 \times 490.8
1. Find the values of the following by using logarithms.(ii)   25.753 \times 0.5341 \times 490.8

1. Find the values of the following by using logarithms.(ii) 25.753 \times 0.5341 \times 490.8

1. Find the characteristics and mantissa of the following Logarithm.(vi) 0.0000300
1. Find the characteristics and mantissa of the following Logarithm.(vi)  0.0000300

1. Find the characteristics and mantissa of the following Logarithm.(vi) 0.0000300

2. Reduce each of the following into a single term.(i) \log _{a} 20-\log _{a} 15+\frac{1}{2} \log _{a} \frac{9}{2}
2. Reduce each of the following into a single term.(i)   \log _{a} 20-\log _{a} 15+\frac{1}{2} \log _{a} \frac{9}{2}

2. Reduce each of the following into a single term.(i) \log _{a} 20-\log _{a} 15+\frac{1}{2} \log _{a} \frac{9}{2}

1. By using table find the numbers whose common logarithms are.(ii) \overline{1} .7427
1. By using table find the numbers whose common logarithms are.(ii)  \overline{1} .7427

1. By using table find the numbers whose common logarithms are.(ii) \overline{1} .7427

Example 01 Write 2^{-4}=\frac{1}{16} in logarithmic form.
Example 01 Write  2^{-4}=\frac{1}{16}  in logarithmic form.

Example 01 Write 2^{-4}=\frac{1}{16} in logarithmic form.

3. If \log 31.09=1.4926 find the value of the following without using \log table.(iv) \log 3109.0
3. If  \log 31.09=1.4926  find the value of the following without using  \log  table.(iv)   \log 3109.0

3. If \log 31.09=1.4926 find the value of the following without using \log table.(iv) \log 3109.0

4. Calculate the following:(i) \log _{3} 2 \times \log _{2} 81
4. Calculate the following:(i)  \log _{3} 2 \times \log _{2} 81

4. Calculate the following:(i) \log _{3} 2 \times \log _{2} 81

2. Express the following numbers in ordinary notation (Standard notation).(iii) 6.018 \times 10^{6}
2. Express the following numbers in ordinary notation (Standard notation).(iii)  6.018 \times 10^{6}

2. Express the following numbers in ordinary notation (Standard notation).(iii) 6.018 \times 10^{6}

1. By using table find the numbers whose common logarithms are.(i) 3.56721
1. By using table find the numbers whose common logarithms are.(i)  3.56721

1. By using table find the numbers whose common logarithms are.(i) 3.56721

3. Find the value of x in the following.(ii) \log _{4} 256=x
3. Find the value of  x  in the following.(ii)  \log _{4} 256=x

3. Find the value of x in the following.(ii) \log _{4} 256=x

1. Find the characteristics and mantissa of the following Logarithm.(i) 8(ii) 5054(iii) 9.992 (vi) 765.3 (v) 0.00329 (vi) 0.0000300
1. Find the characteristics and mantissa of the following Logarithm.(i) 8(ii) 5054(iii)  9.992 (vi)  765.3 (v)  0.00329 (vi)  0.0000300

1. Find the characteristics and mantissa of the following Logarithm.(i) 8(ii) 5054(iii) 9.992 (vi) 765.3 (v) 0.00329 (vi) 0.0000300

1. Express the following logarithm in terms of \log _{a} x \log _{a} y and \log _{a} z .(v) \log _{a} \frac{\sqrt[6]{x y^{-1} z^{-2}}}{\left(x^{-1} y^{-2} z^{-3}\right)^{\frac{1}{6}}}
1. Express the following logarithm in terms of  \log _{a} x \log _{a} y  and  \log _{a} z .(v)  \log _{a} \frac{\sqrt[6]{x y^{-1} z^{-2}}}{\left(x^{-1} y^{-2} z^{-3}\right)^{\frac{1}{6}}}

1. Express the following logarithm in terms of \log _{a} x \log _{a} y and \log _{a} z .(v) \log _{a} \frac{\sqrt[6]{x y^{-1} z^{-2}}}{\left(x^{-1} y^{-2} z^{-3}\right)^{\frac{1}{6}}}

1. Write the following into sum or difference.(ii) \log \frac{15.2}{30.5}
1. Write the following into sum or difference.(ii)  \log \frac{15.2}{30.5}

1. Write the following into sum or difference.(ii) \log \frac{15.2}{30.5}

1. Find the values of the following by using logarithms.(x) \frac{(43.68)^{5} \times \sqrt{(0.057)^{3}}}{(3.048)^{4}}
1. Find the values of the following by using logarithms.(x)  \frac{(43.68)^{5} \times \sqrt{(0.057)^{3}}}{(3.048)^{4}}
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1. Find the values of the following by using logarithms.(x) \frac{(43.68)^{5} \times \sqrt{(0.057)^{3}}}{(3.048)^{4}}

2. Find the logarithms of the following numbers.(i) 9
2. Find the logarithms of the following numbers.(i) 9
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2. Find the logarithms of the following numbers.(i) 9

2. Express the following numbers in ordinary notation (Standard notation).(ix) 3.056 \times 10^{6} \mathrm{~d}
2. Express the following numbers in ordinary notation (Standard notation).(ix)  3.056 \times 10^{6} \mathrm{~d}
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2. Express the following numbers in ordinary notation (Standard notation).(ix) 3.056 \times 10^{6} \mathrm{~d}

Example 02 Find the log of the following numbers:(i) 278.27
Example 02 Find the log of the following numbers:(i)  278.27
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Example 02 Find the log of the following numbers:(i) 278.27

2. Find the Logarithm of the following numbers by using calculator.(v) 0.00851
2. Find the Logarithm of the following numbers by using calculator.(v)  0.00851
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2. Find the Logarithm of the following numbers by using calculator.(v) 0.00851

2. Fill in the blanks.(iv) \log 512=
2. Fill in the blanks.(iv)  \log 512=
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2. Fill in the blanks.(iv) \log 512=

1. Find the values of the following by using logarithms.(i) 57.86 \times 4.385
1. Find the values of the following by using logarithms.(i)   57.86 \times 4.385
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1. Find the values of the following by using logarithms.(i) 57.86 \times 4.385

1. Express the following logarithm in terms of \log _{a} x \log _{a} y and \log _{a} z .(iv) \log _{a}\left\{\left(\frac{y z^{-2}}{y^{-4} z^{3}}\right)^{-3} \div\left(\frac{y^{-1} z}{y^{2} z^{-3}}\right)^{5}\right\}
1. Express the following logarithm in terms of  \log _{a} x \log _{a} y  and  \log _{a} z .(iv)  \log _{a}\left\{\left(\frac{y z^{-2}}{y^{-4} z^{3}}\right)^{-3} \div\left(\frac{y^{-1} z}{y^{2} z^{-3}}\right)^{5}\right\}
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1. Express the following logarithm in terms of \log _{a} x \log _{a} y and \log _{a} z .(iv) \log _{a}\left\{\left(\frac{y z^{-2}}{y^{-4} z^{3}}\right)^{-3} \div\left(\frac{y^{-1} z}{y^{2} z^{-3}}\right)^{5}\right\}

1. Find the values of the following by using logarithms.(vii) \sqrt[5]{2.709} \times \sqrt[7]{1.239}
1. Find the values of the following by using logarithms.(vii)  \sqrt[5]{2.709} \times \sqrt[7]{1.239}
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1. Find the values of the following by using logarithms.(vii) \sqrt[5]{2.709} \times \sqrt[7]{1.239}

1. Express the following logarithm in terms of \log _{a} x \log _{a} y and \log _{a} z .(i) \log _{a} \frac{x^{3} y}{z^{2}}
1. Express the following logarithm in terms of  \log _{a} x \log _{a} y  and  \log _{a} z .(i)  \log _{a} \frac{x^{3} y}{z^{2}}
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1. Express the following logarithm in terms of \log _{a} x \log _{a} y and \log _{a} z .(i) \log _{a} \frac{x^{3} y}{z^{2}}

1. Use log tables to find the value of(iii) \frac{0.678 \times 9.01}{0.0234}
1. Use log tables to find the value of(iii)  \frac{0.678 \times 9.01}{0.0234}
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1. Use log tables to find the value of(iii) \frac{0.678 \times 9.01}{0.0234}