Answer:
Option A - Power property
Step-by-step explanation:
Given : Expression [tex]\log \sqrt[6]{25x^2}=\frac{1}{3}\log 5x[/tex]
To find : Choose the property used to rewrite the expression?
Solution :
First we rewrite or solve the expression again.
Taking LHS of the given expression and solve,
[tex]LHS=\log \sqrt[6]{25x^2}[/tex]
Solving power by property,
i.e, [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]
[tex]=\log [(5x)^2]^\frac{1}{6}[/tex]
[tex]=\log [(5x)]^\frac{1}{3}[/tex]
Apply logarithmic power property,
i.e, [tex]\log a^x=x\log a[/tex]
[tex]=\frac{1}{3}\log 5x=RHS[/tex]
Therefore, The property used to solve the given expression is Power property.
Therefore, Option A is correct.
