Question

Which properties would be used to solve the logarithmic expression

Answer 1

ANSWER

C. Power rule

E. Equality rule

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:

$\begin{gathered} 3\log y=\frac{1}{2}\log x \\ \log y^3=\log x^{1/2} \end{gathered}$

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:

$y=x^{1/6}$