Aus Online Mathematik Brückenkurs 1

The logarithm \displaystyle \text{lg 46 } satisfies the relation

\displaystyle \text{10}^{\text{lg 46 }}=46

and taking the natural logarithm of both sides, we obtain

\displaystyle \ln \text{10}^{\text{lg 46 }}=\ln 46

If we use the logarithm law, \displaystyle \lg a^{b}=b\centerdot \lg a, on the left-hand side, the equality becomes

\displaystyle \lg 46\centerdot \ln 10=\ln 46

This shows that

\displaystyle \lg 46=\frac{\ln 46}{\ln 10}=\frac{3.828641}{2.302585}=1.6627578

and the answer is \displaystyle \text{1}.\text{663}.

NOTE: In order to calculate the answer on a calculator, you press

\displaystyle \begin{align} & \left[ 4 \right]\quad \left[ 6 \right]\quad \left[ \text{LN} \right]\quad \left[ \div \right]\quad \left[ 1 \right]\quad \left[ 0 \right]\quad \left[ \text{LN} \right]\quad \left[ = \right] \\ & \quad \\ \end{align}