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

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

Feb 8, 2015

#1
+27377
+10

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

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

.

Feb 8, 2015

#1
+27377
+10

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

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

.

Alan Feb 8, 2015