Find each value. If applicable, give an approximation to four decimal places. See Example 1. . log 63

Verified step by step guidance

1. Step 1: Understand that the problem is asking for the logarithm of 63, which is written as \( \log_{10}(63) \). This is the common logarithm, meaning the base is 10.
2. Step 2: Recognize that \( \log_{10}(63) \) is asking the question: 'To what power must 10 be raised to get 63?'
3. Step 3: Use a calculator to find \( \log_{10}(63) \). Most scientific calculators have a 'log' button that can be used to find this value directly.
4. Step 4: Enter 63 into the calculator and press the 'log' button to compute the logarithm.
5. Step 5: The calculator will provide a decimal value. If needed, round this value to four decimal places to get the final approximation.

Key Concepts

Logarithms

A logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised to produce a given number? For example, log base 10 of 100 is 2, since 10^2 = 100. Understanding logarithms is essential for solving problems involving exponential growth or decay.

Base of a Logarithm

The base of a logarithm determines the number system used for the logarithmic calculation. Common bases include 10 (common logarithm) and e (natural logarithm). The choice of base affects the value of the logarithm, so it's important to identify the base when solving logarithmic equations.

Approximation and Rounding

Approximation involves estimating a value to a certain degree of accuracy, often rounding to a specified number of decimal places. In this context, approximating log 63 to four decimal places means finding a value close to the actual logarithm and expressing it with four digits after the decimal point, which is crucial for precision in calculations.