write 5 log x-(3 log y + log z) as a simple logrithm

To simplify the expression \( 5 \log x - (3 \log y + \log z) \), we can use logarithmic properties:

1. Use the property \( a \log b = \log b^a \):
   \[
   5 \log x = \log x^5
   \]

2. Rewrite the subtraction using the property \( \log a - \log b = \log \frac{a}{b} \):
   \[
   3 \log y + \log z = \log(y^3) + \log z = \log(y^3 z)
   \]

3. Now substitute back into the expression:
   \[
   5 \log x - (3 \log y + \log z) = \log x^5 - \log(y^3 z)
   \]

4. Use the subtraction property again:
   \[
   = \log \frac{x^5}{y^3 z}
   \]

So, the simplified expression is:
\[
\log \frac{x^5}{y^3 z}
\]

If you need further details or have any questions, let me know! Here are some related questions to consider:

1. What are the properties of logarithms that are most useful for simplification?
2. Can you provide examples of other logarithmic identities?
3. How does the base of the logarithm affect its properties?
4. What is the difference between natural logarithms and common logarithms?
5. How can logarithmic equations be solved? 

**Tip:** Always remember to apply logarithmic properties systematically to simplify expressions effectively.

write 5 log x-(3 log y + log z) as a simple logarithm

Discover how to simplify the expression 5 log x - (3 log y + log z) into a single logarithm using key logarithmic properties. This step-by-step solution is ideal for high school students learning about logarithms.

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