Answered

choose the property used to rewrite the expression. log ^6sqrt(25x^2)=1/3log5x

APower Property

BCommutative Property

CProduct Property

DQuotient Property

Verified Answer :

Answer:

Option A - Power property

Step-by-step explanation:

Given : Expression  \(\log \sqrt[6]{25x^2}=\frac{1}{3}\log 5x\)

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,

\(LHS=\log \sqrt[6]{25x^2}\)      

Solving power by property,

i.e, \(\sqrt[n]{x}=x^{\frac{1}{n}}\)

\(=\log [(5x)^2]^\frac{1}{6}\)    

\(=\log [(5x)]^\frac{1}{3}\)        

Apply logarithmic power property,  

i.e,  \(\log a^x=x\log a\)  

\(=\frac{1}{3}\log 5x=RHS\)  

Therefore, The property used to solve the given expression is Power property.

Therefore, Option A is correct.

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