- 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 we can’t use calculators, we have to simplify this expression. So what rules and identities do we know for logarithms?

- If \(\lg 2 = 0.30103\) and \(\lg 3 = 0.47712\), find, without using tables [or calculators], the values of \(\lg 6\) and \(\lg 15\).

How could we rewrite the required logarithms in terms of the logarithms we are given? Remember that all logarithms are to base 10!