Question

Pre calculus 3a. show that log,2x = 1/2logr, x where r, x € R^+3b. It is given that log2y + log42x = 0Express Y in terms of X. Give your answer in the form y = px^q where p, q are constants.

Answer 1

3a. Answer:

`\log _(r^2)(x)`

Applying the properties of logarithms

`\log _(a^b)(x)=(1)/(b)\log _a(x)\text{ assume }a\ge0`

Therefore, in this case:

`=(1)/(2)\log _r(x)`

3b. Given

`\log _2(y)+\log _4(x)+\log _4(2x)=0`

So, clear for y:

`\begin{gathered} \log _2(y)+\log _4(2x^2)=0 \\ \log _2(y)+(1)/(2)\log _2(2x^2)=0 \\ \log _2(y)=-(1)/(2)\log _2(2x^2) \\ \log _2(y)=\log _2(\frac{1}{\sqrt[]{2x}}) \\ y=\frac{1}{\sqrt[]{2}}x^(-1) \end{gathered}`

Answer:

`y=\frac{1}{\sqrt[]{2}}x^(-1)`