Thread: Simplify

(1/5)^3y=0.008 then $\displaystyle (0.025)^y$ will be
(a)0.25
(b)0.0625
(c)0.125

Originally Posted by devi

$\displaystyle (1/5)^3y=0.008$ then $\displaystyle (0.025)^y$ will be
(a)0.25
(b)0.0625
(c)0.125

solve for y in the first equation, and then plug in its value into the second to find its value

can you solve for y?

Originally Posted by Jhevon

solve for y in the first equation, and then plug in its value into the second to find its value

can you solve for y?

If that is the correct equation, then the answer wouldn't match any of the choices...

--Chris

Originally Posted by Chris L T521

If that is the correct equation, then the answer wouldn't match any of the choices...

--Chris

Perhaps (a) should've been 0.025

Originally Posted by Chris L T521

If that is the correct equation, then the answer wouldn't match any of the choices...

--Chris

The answer is given as 0.25
It is whole power 3y

Given: $\displaystyle (\frac{1}{5})^{3y}=0.008$

Take the log (unspecified base, but same base on both sides.) of both sides: $\displaystyle \log{(\frac{1}{5})^{3y}} = \log{0.008}$

Carry down 3y: $\displaystyle 3y \cdot \log{\frac{1}{5}} = \log{0.008}$

Divide by 3 and $\displaystyle \log{\frac{1}{5}}$ on both sides: $\displaystyle y = \frac{\log{0.008}}{3 \cdot \log{\frac{1}{5}}}$

y = ...

Originally Posted by devi

(1/5)^3y=0.008 then $\displaystyle (0.025)^y$ will be
(a)0.25
(b)0.0625
(c)0.125

Well, $\displaystyle \tfrac{1}{5}^{3y}=.008\implies \tfrac{1}{125}^y=.008$

However, $\displaystyle .008=\tfrac{1}{125}$, so we get the expression $\displaystyle \tfrac{1}{125}^y=\tfrac{1}{125}$

The only value of y that causes this expression to be true is $\displaystyle y=1$

But then $\displaystyle (0.025)^y\implies(0.025)^1=0.025$...

However, this isn't one of the solutions...

--Chris

Originally Posted by Chris L T521

Well, $\displaystyle \tfrac{1}{5}^{3y}=.008\implies \tfrac{1}{125}^y=.008$

However, $\displaystyle .008=\tfrac{1}{125}$, so we get the expression $\displaystyle \tfrac{1}{125}^y=\tfrac{1}{125}$

The only value of y that causes this expression to be true is $\displaystyle y=1$

But then $\displaystyle (0.025)^y\implies(0.025)^1=0.025$...

However, this isn't one of the solutions...

--Chris

i concur. the final answer is 0.025

Originally Posted by devi

(1/5)^3y=0.008 then $\displaystyle (0.025)^y$ will be
(a)0.25
(b)0.0625
(c)0.125

Solution:

$\displaystyle (1/5)^3y= 0.008$
$\displaystyle (1/5)^3y = (0.2)^3$
$\displaystyle (0.2)^3y = (0.2)^3$
y=1

Now
$\displaystyle (0.025)^y$
=$\displaystyle (0.025)^1$
=0.025