Answer:
\(\frac{1}{2}log13-\frac{1}{2}log74\) is the expansion of the given logarithmic function.
Step-by-step explanation:
We have been given an expression:
\(log_b\sqrt{\frac{13}{74}}\)
Since, we know \(\sqrt{x}=x^\frac{1}{2}\)
The given expression can be rewritten as:
\(log_b(\frac{13}{74})^\frac{1}{2}\)
Now, using logarithmic property:
\(log m^n=nlogm\) so we get:
\(\frac{1}{2}log_b\frac{13}{74}\)
Now, using \(log\frac{m}{n}=logm-logn\)
Here, m=13 and n=74
\(\frac{1}{2}log13-\frac{1}{2}log74\) is the expansion of the given logarithmic function.
