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