Pre-Calculus Prep: Evaluating Logarithms

Evaluating logarithms is an important skill in pre-calculus. Logarithms allow us to solve equations and work with exponential functions. To evaluate logarithms, follow these steps:

1. Identify the logarithmic expression: Start by identifying the given logarithmic expression that you need to evaluate. It should have the form log_b(x), where 'b' is the base of the logarithm and 'x' is the value inside the logarithm.

2. Determine the base: Identify the base 'b' of the logarithm. Common bases include 10 (logarithm base 10, often denoted as log(x)), e (natural logarithm, denoted as ln(x)), or any other specified base.

3. Substitute the value: Replace 'x' in the logarithmic expression with the given value you want to evaluate. This will give you an expression like log_b(value).

4. Evaluate the logarithm: Use the properties of logarithms and your knowledge of the specific base to evaluate the logarithm expression. For example:

- If the base is 10 (logarithm base 10): Use the power of 10 to evaluate the logarithm. For instance, log(100) = 2 because 10^2 = 100.

- If the base is e (natural logarithm): Use the exponential function e^x to evaluate the logarithm. For example, ln(e^2) = 2 because e^(ln(e^2)) = e^2 = value.

- If the base is a different specified value: Apply the properties of logarithms specific to that base to evaluate the logarithm. For instance, log_2(8) = 3 because 2^3 = 8.

5. Express the result: Write down the evaluated logarithm in its final form, taking into account any specific base or notation requirements.

Remember that logarithms are the inverse operations of exponential functions. Evaluating logarithms allows us to find the exponent needed to produce a given value using a specific base.

These videos are designed to review and reteach Precalculus and Collegeboard Pre-CALC AP content. My videos cover functions, polynomials, exponential and logarithmic expressions, trigonometry, parametric equations, polar coordinates, vectors, matrices and systems, conic sections, discrete mathematics, sequences and series; and an introduction to calculus.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa .
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