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

Verified step by step guidance

Recognize that the expression \( \log 63 \) typically means the logarithm base 10 of 63, which is written as \( \log_{10} 63 \).

Recall the definition of logarithm: \( \log_b a = c \) means \( b^c = a \). Here, we want to find \( c \) such that \( 10^c = 63 \).

Use the change of base formula if needed: \( \log_b a = \frac{\log_k a}{\log_k b} \). Since the base is 10, you can directly use a calculator or logarithm tables to find \( \log_{10} 63 \).

If you are calculating by hand or using a calculator, input 63 and press the \( \log \) button to get the value.

If an approximation is required, round the result to four decimal places.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Definition of Logarithms

A logarithm answers the question: to what exponent must the base be raised to produce a given number? For example, log_b(a) = c means b^c = a. Understanding this definition is essential to interpret and solve logarithmic expressions.

Common Logarithms (Base 10)

When the base is not specified, log usually refers to the common logarithm with base 10. This means log 63 is log_10(63). Knowing this helps in using calculators or logarithm tables to find approximate values.

Using a Calculator for Logarithms

Calculators typically have a log button for base-10 logarithms. To find log 63, input 63 and press log to get a decimal approximation. Rounding the result to four decimal places provides the required precision.

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