https://file.aiquickdraw.com/mathbot/file/1726718705396g1o5cm9q.jpg

Let's solve the logarithmic problems presented in the image:

1. **a. \( \log_2 32 \)**

   To solve \( \log_2 32 \), we need to determine the power to which 2 must be raised to get 32:
   \[
   2^5 = 32
   \]
   Hence, \( \log_2 32 = 5 \).

2. **b. \( \log_7 \left(\frac{1}{343}\right) \)**

   We know that \( 343 = 7^3 \). Since the logarithm involves a reciprocal, we can apply the property:
   \[
   \log_b \left(\frac{1}{x}\right) = -\log_b(x)
   \]
   Therefore,
   \[
   \log_7 \left(\frac{1}{343}\right) = -\log_7(343) = -3
   \]
   because \( 7^3 = 343 \).

3. **c. \( \log 10000 \)**

   Since no base is specified, we assume this is the common logarithm (base 10). We know that:
   \[
   10^4 = 10000
   \]
   Hence, \( \log 10000 = 4 \).

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Let me know if you need more details on any step!

**Relative questions:**

1. How do you calculate logarithms with different bases?
2. What are the key properties of logarithms?
3. How can you simplify expressions involving \( \log_b (1/x) \)?
4. What is the difference between common logarithms and natural logarithms?
5. How do you solve logarithmic equations involving multiple terms?

**Tip:** Remember that the base of a logarithm determines how fast the function grows or shrinks. For example, \( \log_2(x) \) grows faster than \( \log_3(x) \).

Tentukan hasil dari bilangan-bilangan berikut: a. log_2 32, b. log_7 (1/343), c. log 10000

Learn how to solve logarithmic equations such as log_2 32, log_7 (1/343), and log 10000. These problems involve logarithmic identities, powers, and reciprocals. Suitable for Grades 10-11.

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