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Exponentials & Logarithms

Review question

Can we evaluate these log expressions without using a calculator?
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Ref: R9976

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Question

Without using tables [or calculators], find the value of \[\begin{align*} 2 \lg 5 - \frac{1}{2} &\lg 9 + \lg 0.12.\\ [\lg x &= \log_{10} x] \end{align*}\]
If \(\lg 2 = 0.30103\) and \(\lg 3 = 0.47712\), find, without using tables [or calculators], the values of \(\lg 6\) and \(\lg 15\).