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you use the properties and laws to find the values os the following logarithmic expression

Let's go through each of the logarithmic expressions from the image and apply the properties and laws of logarithms to find their values.

### 1. \( \log 10 \)
Using the logarithmic property:
\[
\log_{10} 10 = 1
\]
This is because any logarithm of the form \( \log_b b \) is equal to 1. This is often called the Identity Law or Law 5.

**Answer**: \( \log 10 = 1 \)

---

### 2. \( \log_4 64 \)
We can express 64 as a power of 4:
\[
64 = 4^3
\]
Using the logarithmic property \( \log_b (b^x) = x \), we get:
\[
\log_4 64 = \log_4 4^3 = 3
\]

**Answer**: \( \log_4 64 = 3 \)

---

### 3. \( \log_5 (125^1) \)
Since \( 125^1 = 125 \), we first note that:
\[
125 = 5^3
\]
Using the logarithmic property \( \log_b (b^x) = x \), we get:
\[
\log_5 125 = \log_5 5^3 = 3
\]

**Answer**: \( \log_5 125^1 = 3 \)

---

### 4. \( 5^{\log_5 2} \)
Here, we apply the property \( b^{\log_b x} = x \). So:
\[
5^{\log_5 2} = 2
\]

**Answer**: \( 5^{\log_5 2} = 2 \)

---

### 5. \( \log 1 \)
Using the property \( \log_b 1 = 0 \), which states that the logarithm of 1 in any base is 0:
\[
\log 1 = 0
\]

**Answer**: \( \log 1 = 0 \)

---

If you have any further questions or want more details, feel free to ask! Here are some additional practice questions to deepen your understanding:

1. What is \( \log_2 32 \)?
2. Simplify \( 2^{\log_2 8} \).
3. Find the value of \( \log_3 81 \) using logarithmic laws.
4. What is the inverse of \( \log_7 x \)?
5. Prove that \( \log_b (x^y) = y \log_b x \).

**Tip**: Remember that converting numbers to powers of the base simplifies logarithmic expressions!

You use the properties and laws to find the values of the following logarithmic expression.

This page guides you through solving logarithmic expressions using logarithmic laws. Learn key properties like log_b(b^x) = x, log_b b = 1, and more. Suitable for high school students in Grades 10-12.

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