If $l o g_{10} a = m$ , express the following in terms of a.
i) $10^{3 m}$
ii) $10^{m + 2}$
iii) $10^{5 m + 3}$

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Solution

Given $l o g_{10} a = m ⟹ a = 10^{m}$

i) $10^{3 m} = (10^{m})^{3} = a^{3}$

ii) $10^{m + 2} = 10^{m} \times 10^{2} = 100 a$

iii) $10^{5 m + 3} = (10^{m})^{5} \times 10^{3} = 1000 a^{5}$

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