Solve each problem. Use a calculator to find an approximation for each logarithm. log 3.984

Verified step by step guidance

1. Recognize that the problem asks for the logarithm of 3.984, which is written as \(\log 3.984\). This typically means the common logarithm, or logarithm base 10.
2. Recall the definition of the common logarithm: \(\log x\) is the exponent to which 10 must be raised to get \(x\). So, \(\log 3.984 = y\) means \$10^y = 3.984$.
3. Since 3.984 is not a power of 10 that we know offhand, use a calculator to find the approximate value of \(\log 3.984\).
4. On your calculator, enter 3.984 and then press the 'log' button to compute the logarithm base 10 of 3.984.
5. Record the decimal approximation given by the calculator as the solution to \(\log 3.984\).

Key Concepts

Logarithms

A logarithm answers the question: to what exponent must a base be raised to produce a given number? For example, log base 10 of 100 is 2 because 10 squared equals 100. Understanding logarithms helps in solving equations involving exponential relationships.

Common Logarithms and Calculator Use

Common logarithms have base 10 and are often denoted simply as log. Calculators typically provide a log button for base-10 logarithms, allowing quick approximation of values like log 3.984. Knowing how to use this function is essential for finding logarithmic values efficiently.

Approximation and Rounding

Since logarithms of non-exact powers often result in irrational numbers, calculators provide decimal approximations. Understanding how to interpret and round these approximations correctly is important for practical applications and ensuring answers are precise to the required degree.