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

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

Therefore, in this case:

$=\frac{1}{2}\log _r(x)$

3b. Given

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

So, clear for y:

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

Answer:

$y=\frac{1}{\sqrt[]{2}}x^{-1}$