$$2yy^{\frac{1}{3}}=0.0002$$
This can be written as:
$$2y^{1\frac{1}{3}}=0.0002$$
Divide both sides by 2
$$y^{1\frac{1}{3}}=0.0001$$
Take log10 of both sides and use the fact that log(xa) = a*log(x):
$$1\frac{1}{3}\log{y}=\log{10^{-4}}$$
as 0.0001 = 10-4
Now log(10-4) is just -4, so
$$1\frac{1}{3}\log{y}=-4$$
or:
$$\frac{4}{3}\log{y}=-4$$
Multiply both sides by 3/4:
$$\log{y}=-3$$
So: y = 10-3 or y = 0.001
.
$$2yy^{\frac{1}{3}}=0.0002$$
This can be written as:
$$2y^{1\frac{1}{3}}=0.0002$$
Divide both sides by 2
$$y^{1\frac{1}{3}}=0.0001$$
Take log10 of both sides and use the fact that log(xa) = a*log(x):
$$1\frac{1}{3}\log{y}=\log{10^{-4}}$$
as 0.0001 = 10-4
Now log(10-4) is just -4, so
$$1\frac{1}{3}\log{y}=-4$$
or:
$$\frac{4}{3}\log{y}=-4$$
Multiply both sides by 3/4:
$$\log{y}=-3$$
So: y = 10-3 or y = 0.001
.