https://file.aiquickdraw.com/mathbot/file/1726447532155j3titelf.jpg

Let's analyze and solve the two logarithmic expressions presented in the image:

### Problem 5: \( 5 \log_5 2 \)

To solve this:
1. The logarithmic part, \( \log_5 2 \), means "the power to which 5 must be raised to get 2." This doesn't simplify directly, so let's leave it in logarithmic form for now.
2. The entire expression is \( 5 \times \log_5 2 \). We can leave the logarithm as is, and the final expression is just \( 5 \log_5 2 \).

For an approximation:
\[
\log_5 2 = \frac{\log 2}{\log 5} \approx \frac{0.3010}{0.69897} \approx 0.43067
\]
Multiplying by 5:
\[
5 \times 0.43067 \approx 2.15335
\]
So the approximate value is **2.15**.

### Problem 6: \( \log 1 \)

For any base \( b \), \( \log_b 1 = 0 \), because any number raised to the power of 0 equals 1:
\[
b^0 = 1
\]
So, the value of \( \log 1 \) is **0**.

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Would you like more details or have any questions on these solutions?

Here are some related questions to deepen your understanding:
1. What is the general form of the logarithmic equation?
2. How do you convert between different logarithmic bases?
3. Why is the logarithm of 1 always 0, regardless of the base?
4. How can logarithms be used in solving exponential equations?
5. What is the change of base formula for logarithms?

**Tip:** Always remember that \( \log_b b = 1 \), because a number raised to the power of 1 is itself.

Find the value of the following logarithmic expressions: 5log₅2 and log 1.

Step-by-step solutions to logarithmic expressions 5log₅2 and log 1. Learn how to apply logarithmic theorems and change of base formula for high school students in Grades 8-10.

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