# Evaluate Logarithms With Integer Base Worksheet

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To evaluate a logarithm with an integer base, express the given logarithmic expression. Convert it to an exponential form where the base raised to the value of the logarithm equals the argument. Compare the exponents and solve for the variable. For example, for log base 3 of 3, convert to 3 raised to what power equals 3, and solve to find the answer is 1.

Algebra 2
Logarithms

## How Will This Worksheet on “Evaluate Logarithms with Integer Base” Benefit Your Student's Learning?

• Working with integer base logarithms helps students understand how numbers can be multiplied to reach another number, crucial for subjects like growth and decay.
• It offers an additional technique to solve math problems and understand numerical relationships.
• Learning these logarithms is important for subjects like calculus, where they are frequently used.
• Practicing logarithms improves problem-solving skills with exponents, enhancing accuracy and speed.
• Using logarithms also supports algebra, benefiting many areas of math and science.

## How to Evaluate Logarithms with Integer Base?

• Identify the given logarithmic expression and state what needs to be found, which is the value of the logarithm.
• Convert the logarithmic form into an equivalent exponential form by expressing the base raised to the logarithm's value equals the argument of the logarithm.
• Once in exponential form, equate the exponents on both sides of the equation, since the bases are the same.
• Solve the resulting equation for the variable, giving us the value of the logarithm.

## Solved Example

Q. Evaluate. $\newline$$\log_3 27$ $\newline$Write your answer in simplest form.
Solution:
1. Rewrite as Power of $3$: Rewrite $27$ as a power of $3$.$\newline$ $27 = 3 \times 3 \times 3$$\newline$ $27 = 3^3$
2. Simplify Logarithm Expression: We found: $27 = 3^3$$\newline$ $\log_3 27$ becomes $\log_3 3^3$
3. Evaluate Logarithm: Evaluate $\log_{3} 3^{3}$.$\newline$ When logarithm base matches exponent base, logarithm equals to exponent.$\newline$ $\log_{3} 3^{3} = 3$

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