Question

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Evaluate logarithmic expressions if possible.
5 log Subscript b Baseline x plus 3 log Subscript b Baseline z
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Part 1
5 log Subscript b Baseline x plus 3 log Subscript b Baseline zequals
  
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Answer 1

To condense the logarithmic expression \(5 \log_b x + 3 \log_b z\), we will use the properties of logarithms.

1. **Property 1**: \(a \log_b m = \log_b m^a\)
This means we can rewrite \(5 \log_b x\) as \(\log_b x^5\) and \(3 \log_b z\) as \(\log_b z^3\).

2. So, we have:
\[
5 \log_b x = \log_b x^5
\]
\[
3 \log_b z = \log_b z^3
\]

3. Now, we can combine these two logarithms using the property: \(\log_b m + \log_b n = \log_b (mn)\):
\[
\log_b x^5 + \log_b z^3 = \log_b (x^5 z^3)
\]

Thus, the expression \(5 \log_b x + 3 \log_b z\) can be condensed to:
\[
\log_b (x^5 z^3)
\]

### Final Answer:
\[
\log_b (x^5 z^3)
\]