To condense the logarithmic expression [tex]\(\log b + z \log d\)[/tex], we can use the properties of logarithms. Here's the detailed step-by-step solution:
1. Identify the properties of logarithms:
- The product rule: [tex]\(\log(a) + \log(b) = \log(ab)\)[/tex]
- The power rule: [tex]\(k \cdot \log(a) = \log(a^k)\)[/tex]
2. Apply the power rule to the term [tex]\(z \log d\)[/tex]:
[tex]\[
z \log d = \log(d^z)
\][/tex]
3. Rewrite the original expression using the result from the power rule:
[tex]\[
\log b + z \log d = \log b + \log(d^z)
\][/tex]
4. Apply the product rule to combine the two logarithms into a single logarithm:
[tex]\[
\log b + \log(d^z) = \log(b \cdot d^z)
\][/tex]
So, the condensed form of the logarithmic expression [tex]\(\log b + z \log d\)[/tex] is:
[tex]\[
\log(b \cdot d^z)
\][/tex]
Final Answer Attempt:
[tex]\[
\log(b \cdot d^z)
\][/tex]
