College Math Placement Practice Test

The logarithm \(\log_{10}(1000)\) can be interpreted as the exponent to which the base \(10\) must be raised to yield the number \(1000\).

To solve this, we need to transform the number \(1000\) into a power of \(10\). We know that \(1000\) can be expressed as \(10^3\). This is because:

\[

10^3 = 10 \times 10 \times 10 = 1000

\]

Since \(1000\) is \(10\) raised to the power of \(3\), we can write the logarithm as:

\[

\log_{10}(1000) = \log_{10}(10^3)

\]

Using the property of logarithms that states \(\log_b(a^n) = n \log_b(a)\) where \(b\) is the base, \(a\) is the argument, and \(n\) is the exponent, we can simplify this to:

\[

\log_{10}(10^3) = 3 \log_{10}(10)

\]

Since \(\log_{10}(10) = 1\