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Which properties would be used to solve the logarithmic expression

Which properties would be used to solve the logarithmic expression-example-1
User Buren
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ANSWER

C. Power rule

E. Equality rule

Step-by-step explanation

The power rule of logarithms is:


\log a^b=b\log a

It can be applied in both ways. This means that in this expression we can put the power back:


\begin{gathered} 3\log y=(1)/(2)\log x \\ \log y^3=\log x^(1/2) \end{gathered}

So first we would use the power rule.

Then, we have log on both sides. The equality rule is:


\begin{gathered} \text{if }\log a=\log b \\ \text{then }a=b \end{gathered}

So for this expression:


\begin{gathered} \log y^3=\log x^(1/2) \\ y^3=x^(1/2) \end{gathered}

So next we would apply the equality rule.

And then we would finish solving the equation:


y=x^(1/6)

User Mikalaj Murziankou
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