Math Problem Statement

Sederhanakan, dan buat cara jalannya

Sederhanakanlah! 2log 16 - 2log 4

Solution

The problem is asking you to simplify the expression:

log216log24\log_2 16 - \log_2 4

Step-by-step Solution:

  1. Apply the properties of logarithms:

    Using the logarithmic property:

    logbalogbc=logb(ac)\log_b a - \log_b c = \log_b \left(\frac{a}{c}\right)

    So,

    log216log24=log2(164)\log_2 16 - \log_2 4 = \log_2 \left(\frac{16}{4}\right)

  2. Simplify the fraction:

    164=4\frac{16}{4} = 4

    Now the expression becomes:

    log24\log_2 4

  3. Simplify the logarithm:

    We know that 4=224 = 2^2, so:

    log24=log2(22)=2\log_2 4 = \log_2 (2^2) = 2

Final Answer:

log216log24=2\log_2 16 - \log_2 4 = 2

Let me know if you would like further details or if you have any questions!

Here are five related questions to expand on this:

  1. How would you simplify log232log28\log_2 32 - \log_2 8?
  2. What is the value of log264log216\log_2 64 - \log_2 16?
  3. Can you apply the same logarithmic properties to solve log381log39\log_3 81 - \log_3 9?
  4. How does the change of base formula help in simplifying logarithms?
  5. Can logarithmic properties be used to simplify products, such as log2(164)\log_2 (16 \cdot 4)?

Tip: When working with logarithms, always remember the key properties like the product, quotient, and power rules. They make simplification much easier!

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Math Problem Analysis

Mathematical Concepts

Logarithms
Properties of Logarithms
Simplification

Formulas

log_b a - log_b c = log_b(a/c)
log_b a^n = n log_b a

Theorems

Properties of Logarithms

Suitable Grade Level

Grades 9-11