Question
Given $\log _{10} \mathrm{x}=2 \mathrm{a}$ and $\log _{10} \mathrm{y}=\frac{b}{2}.$ Write $10^{2 \mathrm{~b}+1}$ in terms of $\mathrm{y}$.
✓
Answer
$ \log _{10} y=\frac{b}{2}$
$ \Rightarrow y=10^{b / 2}$
$ \Rightarrow y^4=10^{2 b}$
$ \Rightarrow 10 y^4=10^{2 b} \times 10$
$ \Rightarrow 10^{2 b+1}$
$=10 y^4$
$ \Rightarrow y=10^{b / 2}$
$ \Rightarrow y^4=10^{2 b}$
$ \Rightarrow 10 y^4=10^{2 b} \times 10$
$ \Rightarrow 10^{2 b+1}$
$=10 y^4$
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