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Logarithms

Obtain the eq...

Question

Obtain the equivalent logarithmic form of the following.
(i) $2^{4} = 16$
(ii) $3^{5} = 243$
(iii) $10^{- 1} = 0.1$
(iv) $8^{- \frac{2}{3}} = \frac{1}{4}$
(v) $25^{\frac{1}{2}} = 5$
(vi) $12^{- 2} = \frac{1}{144}$

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Solution

(i) ${log}_{2} 16 = 4$

(ii) ${log}_{3} 243 = 5$

(iii) ${log}_{10} 0.1 = - 1$

(iv) ${log}_{8} \frac{1}{4} = \frac{- 2}{3}$

(v) ${log}_{25} 5 = \frac{1}{2}$

(vi) ${log}_{12} (\frac{1}{144}) = - 2$

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Q. Obtain the equivalent exponential form of the following.
(i)

{log}_{6} 216 = 3

{log}_{9} 3 = \frac{1}{2}

{log}_{5} 1 = 0

{log}_{\sqrt{3}} 9 = 4

{log}_{64} (\frac{1}{8}) = - \frac{1}{2}

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Q. Simplify the following.
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Q. Change the following from logarithmic form to exponential form.
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{log}_{4} 64 = 3

{log}_{16} 2 = \frac{1}{4}

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Q. Simplify:

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\sqrt[3]{(343)^{- 2}}

(0.001)^{1 / 3}

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{(\frac{\sqrt{2}}{5})}^{8} \div {(\frac{\sqrt{2}}{5})}^{13}

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Q. Simplify:
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