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Common Logs Solutions

• The common logarithm has a    base of 10   . Recall that when the base is not written for a logarithm, it is understood to be 10.
• It can be written as ${\log }_{10}x$ or, most commonly,    log x   .

• You can    estimate    the approximate value of a log without technology when you ask yourself:

  • “Ten to what power is    nearest    to the given argument?”

    or

  • “   Between    which two whole numbers is the argument?”

Example 1

The approximate value of $\mathbf{log} \mathbf{72}$ is between which two integers? To which integer is the value closest? Explain. Do not use technology. 

Example 2

The approximate value of $\mathbf{log}\frac{\mathbf{1}}{\mathbf{450}}$ is between which two integers? Explain.

$$\begin{gathered} {10}^x=\frac{1}{450} \\ {10}^{–2}=\frac{1}{100} {10}^{–3}=\frac{1}{1000} \end{gathered}$$

For $\log \frac{1}{450}$, x is between    –3 and –2    because $\frac{1}{450}$ is between $\frac{1}{100}$ and $\frac{1}{1000}$.