Answer:
Yes the answer is correct explained in step-by-step explaination.
Step-by-step explanation:
Given the logarithmic expression
log(base b)square root 57/74
\(\log_{b}\frac{\sqrt57}{74}\)
Now we know that \(\log \frac{m}{n} =\log m-\log n\\\log x^{\frac{1}{2} } =\frac{1}{2}\log x\)
Hence, \(log _{b}\sqrt57=\frac{1}{2}log _{b}57\)
∴\(log_{b}\frac{\sqrt57 }{74}=log_{b}{\sqrt57 }-log_{b}{54}\)
\(\frac{1}{2}log_{b}57-log_{b}54\)
