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
[tex]\log_{b}\frac{\sqrt57}{74}[/tex]
Now we know that [tex]\log \frac{m}{n} =\log m-\log n\\\log x^{\frac{1}{2} } =\frac{1}{2}\log x[/tex]
Hence, [tex]log _{b}\sqrt57=\frac{1}{2}log _{b}57[/tex]
∴[tex]log_{b}\frac{\sqrt57 }{74}=log_{b}{\sqrt57 }-log_{b}{54}[/tex]
[tex]\frac{1}{2}log_{b}57-log_{b}54[/tex]
