MHB How Can You Rewrite an Equation to Express y as a Function of x?

[karush]

$\tiny{6.5.95 Kamehameha HS}$

Express y as a function of x. $\quad C>0$
$3\ln{y}=\dfrac{1}{2}\ln{(2x+1)}-\dfrac{1}{3}\ln{(x+4)}+\ln{C}$
rewirte as
$\ln{y^3}=\ln{(2x+1)^{(1/2)}}-\ln{(x+4)^{(1/3)}}+\ln{C}$
then e thru and isolate y
i think
looks like it will be ugly

 

[skeeter]

$y = \dfrac{C_2\sqrt[6]{2x+1}}{\sqrt[9]{x+4}}$

 

[HOI]

$\tiny{6.5.95 Kamehameha HS}$

Express y as a function of x. $\quad C>0$
$3\ln{y}=\dfrac{1}{2}\ln{(2x+1)}-\dfrac{1}{3}\ln{(x+4)}+\ln{C}$
rewirte as
$\ln{y^3}=\ln{(2x+1)^{(1/2)}}-\ln{(x+4)^{(1/3)}}+\ln{C}$

I would have said, instead,
$ln(y)= \ln((2x+1)^{1/6})- \ln((x+4)^{1/9})+ ln(C)$
and then use the properties of the logarithm
$ln(y)= \ln\left(\frac{C(2x+1)^{1/6}}{(x+ 4)^{1/9}}\right)$

then e thru and isolate y
i think
looks like it will be ugly

Now, it doesn't look so ugly!

 

[karush]

well that certainly helped a lot
pays to get more input