Help with algebra

victoria0212

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Feb 13, 2020
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Can someone please show and explain how to solve this? I'm not sure if I'm doing it right.
Here's it is: Write 323∙√3 as a exponent with the base 3. Use the exponent laws. No calculator.
 

pka

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Jan 29, 2005
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Can someone please show and explain how to solve this? I'm not sure if I'm doing it right.
Here's it is: Write 323∙√3 as a exponent with the base 3. Use the exponent laws. No calculator.
This is a very odd question. Is it copied correctly? Answer as written: \(323\cdot 3^{\tfrac{1}{2}}\)
 

firemath

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Oct 29, 2019
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Hello, and welcome to Free Math Help!

Do you know your exponent laws?

Here is one hint: Another way to write the square root of 3 is \(\displaystyle 3^{1/2}\).
 

firemath

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This is a very odd question. Is it copied correctly? Answer as written: \(323\cdot 3^{\tfrac{1}{2}}\)
Sorry, @pka...stepped on your toes.
 

Romsek

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Nov 16, 2013
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Your wording is a bit confusing.

Maybe you mean

\(\displaystyle 323 \cdot \sqrt{3} = 3^{\left(\frac 1 2 + \log_3(323)\right)}\) ?

To see this

by definition of logs \(\displaystyle 3^{\log_3(323)} = 323\)

\(\displaystyle \sqrt{3} = 3^{\frac 1 2}\)

combining these we get the expression above.
 

victoria0212

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Feb 13, 2020
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5
Your wording is a bit confusing.

Maybe you mean

\(\displaystyle 323 \cdot \sqrt{3} = 3^{\left(\frac 1 2 + \log_3(323)\right)}\) ?

To see this

by definition of logs \(\displaystyle 3^{\log_3(323)} = 323\)

\(\displaystyle \sqrt{3} = 3^{\frac 1 2}\)

combining these we get the expression above.
I have actually no idea. This is how it was written but I don't quite understand it.
 

firemath

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Oct 29, 2019
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I think it's just a multiplication problem that needs a product written as a power of 3.
 

victoria0212

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Feb 13, 2020
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I think it's just a multiplication problem that needs a product written as a power of 3.
Now that I've been thinking about this for a while and done my research, I think I finally get it. Thanks!!
 

Subhotosh Khan

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Jun 18, 2007
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Now that I've been thinking about this for a while and done my research, I think I finally get it. Thanks!!
Could you share your answer so that a student in future can be helped?
 
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