2y times y^1/3=.0002 solve for y

$$2yy^{\frac{1}{3}}=0.0002$$

 

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(x^a) = 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

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