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Logarithms — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSLogarithms2 Marks
Question
If $log_{10}a = b,$ find $10^{3b - 2}$ in terms of a.
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Answer

$ \log _{10} \mathrm{a}=\mathrm{b}$
$ \Rightarrow 10^{\mathrm{b}}=\mathrm{a}$
$ \Rightarrow\left(10^{\mathrm{b}}\right)^3=\mathrm{a}^3 \ldots[\text { Cubing both sides ] }$
$ \Rightarrow \frac{10^{3 b}}{10^2}=\frac{a^3}{10^2} \ldots\left[\text { dividing both sides by } 10^2\right]$
$ \Rightarrow 10^{3 \mathrm{~b}-2}=\frac{a^3}{100}$

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