(probably) Fairly easy equation that I can't do: solve 1/(cbrt(5))^2 = 5^n

Schmitz

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So, I don't know how to work this one out. Can anybody point me in the right direction? It's due tomorrow, and I have to get this right. Thank you in advance.

. . .\(\displaystyle \large \mbox{Find the value of }\, n:\)

. . . . .\(\displaystyle \large \dfrac{1}{\left(\sqrt[3]{\strut 5\,}\right)^2}\, =\, 5^n\)

I've worked out that the answer to the equation in the denominator of the fraction is 2.92. I thought that I needed to cycle through all of the roots of 5 until I found 2.92, until I realised that that isn't the case. I don't really know what to do now, so any help would be appreciated.
 

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So, I don't know how to work this one out. Can anybody point me in the right direction? It's due tomorrow, and I have to get this right. Thank you in advance.



1/3^
√5)^2 = 5^n

Find the value of n


(I think I typed that really badly but oh well

Is your problem:

\(\displaystyle \displaystyle{\left[\left[\dfrac{1}{3}\right]^{\sqrt 5}\right]^2 \ = \ 5^n}\)

Find the value of n

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33
 
Is your problem:

\(\displaystyle \displaystyle{\left[\left[\dfrac{1}{3}\right]^{\sqrt 5}\right]^2 \ = \ 5^n}\)

Find the value of n

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

Ok, I'll edit my post in order to make it a bit clearer, and I'll try to convey what I've got so far.
 
Hi. You need to work with exact values, in this exercise, so don't try to evaluate the radical as a decimal approximation.

Instead, rewrite the radical-squared (the denominator) in exponential form. There's a property for that which I'm guessing you've been shown in class or in your materials.

Once you've expressed the denominator as 5 raised to a fraction, then multiply both sides of the equation by the denominator.

Then you will have two powers of 5 multiplied together on one side and the number 1 on the other side.

Multiply the two powers of 5 together symbolically, using the property of exponents that you've learned, and hopefully you'll then recognize what that symbolic exponent must be, in order for that power of 5 to equal 1.

If this is too many steps for you to understand at once, then just do the first one (rewrite the radical-squared in exponential form), and show us your work. We can go from there. :)
 
So, I don't know how to work this one out. Can anybody point me in the right direction? It's due tomorrow, and I have to get this right. Thank you in advance.


attachment.php


I've worked out that the answer to the equation in the denominator of the fraction is 2.92. I thought that I needed to cycle through all of the roots of 5 until I found 2.92, until I realised that that isn't the case. I don't really know what to do now, so any help would be appreciated.

\(\displaystyle \displaystyle{\sqrt[3]{5} \ = \ 5^x}\) → x = ?

\(\displaystyle \displaystyle{\left (\sqrt[3]{5}\right )^2 \ = \ 5^y}\) → y = ?

\(\displaystyle \displaystyle{\dfrac{1}{\left (\sqrt[3]{5}\right )^2} \ = \ 5^n}\) → n = ?
 
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